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Case Study Questions for Class 8 Maths Chapter 10 Visualising Solid Shapes

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Here we are providing Case Study questions for Class 8 Maths Chapter 10 Visualising Solid Shapes.

Visualising Solid Shapes Case Study Questions

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Visualising Solid Shapes

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Learn Visualizing Solid Shapes free at Teachoo. All NCERT Exercise Questions and Examples have been solved in easy to understand way. Concepts of the chapter is also explained in the Concept wise section.

In previous classes we studied about 2D and 3D shapes. Two Dimensional Shapes have length and breadth. Whereas, Three Dimensional Shapes have Length, Breadth and Height.

We studied 3D shapes like Cube, Cuboid, Cone, Cylinder, Prism, Sphere, Hemisphere

But, in reality

3D Shapes are a combination of shapes. Like: Ice cream Cone has Cone at bottom, and hemisphere on top. 

In this chapter, we will study

• Top View, Front View, Side View of 3 Dimensional Objects
• Then, we will learn how to draw and label a map.
• And what scale in a map is
• Then, we learn what a Polyhedron is
• And what is a convex , not-convex and a regular polyhedron
• The difference between Prism and Pyramid
• Then, we will study how to find Faces ( F ), Edges ( E ) and Vertices ( V ) of different polyhedrons
• And learn about Euler's Formula - F + V - E = 2

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NCERT Solutions Class 8 Maths Chapter 10 Visualising Solid Shapes

NCERT solutions for class 8 maths Chapter 10 Visualising Solid Shapes explores the difference between two-dimensional and three-dimensional figures. The plain shapes having only length and breadth are called two-dimensional shapes, whereas the figures which possess length, breadth, and height are called three-dimensional shapes . The NCERT solutions class 8 maths Chapter 10 explains how any solid shape occupies space. Two-dimensional figures include triangles , rectangles , and circles , whereas three-dimensional figures include cylinders , cubes, cones , and spheres .

A three-dimensional object can appear different from different angles , allowing for a variety of views to be drawn. In this chapter, kids are introduced to a variety of combinatorial shapes that are closer to the form taken by many solid figures in real life. The pdf of class 8 maths NCERT solutions chapter 10 Visualising Solid Shapes is given below and also you can find some of these in the exercises given below.

• NCERT Solutions Class 8 Maths Chapter 10 Ex 10.1
• NCERT Solutions Class 8 Maths Chapter 10 Ex 10.2
• NCERT Solutions Class 8 Maths Chapter 10 Ex 10.3

NCERT Solutions for Class 8 Maths Chapter 10 PDF

Solid geometry has a widespread role in everyday life as it helps in getting an idea of the different shapes surrounding us and their properties. Good knowledge of visualizing solids will not only help the students in understanding the further complex geometry topics but also in solving real-world problems. The pdf of the NCERT Solutions Class 8 Maths Chapter 10 Visualising Solid Shapes is given below :

☛ Download Class 8 Maths NCERT Solutions Chapter 10

NCERT Class 8 Maths Chapter 10   Download PDF

NCERT Solutions for Class 8 Maths Chapter 10

At times shapes that we see are not necessarily triangle, square, or rectangle, but a combination of them. A study of NCERT Solutions Class 8 Maths Chapter 10 Visualising Solid Shapes will help in identifying such combinations of shapes by visualizing the individual shapes forming them. A quick glance at the questions in each section of the chapter can be seen below

• Class 8 Maths Chapter 10 Ex 10.1 - 4 Questions
• Class 8 Maths Chapter 10 Ex 10.2 - 4 Questions
• Class 8 Maths Chapter 10 Ex 10.3 - 8 Questions

☛ Download Class 8 Maths Chapter 10 NCERT Book

Topics Covered: The class 8 maths NCERT solutions Chapter 10 talks about the objects in the 2D and the 3D space, their views from different perspectives in case of three-dimension, mapping of surrounding areas, the concept of a polyhedron, their types, and Euler's formula .

Total Questions: The Class 8 maths Chapter 10 Visualising Solid Shapes Chapter 10 consists of total 16 questions of which 10 are easy, 2 are moderate and, 4 are long answer type questions.

List of Formulas in NCERT Solutions Class 8 Maths Chapter 10

The NCERT solutions class 8 maths Chapter 10 covers the important aspects of objects in space. The comprehension of the various solid shapes is important, be it in two-dimension or three-dimension as it helps us in understanding our world better. Some important facts and formulas regarding the same have been covered in NCERT solutions for class 8 maths Chapter 10, a few of which are as given below :

• An object in a three-dimensional space can have various shapes when viewed from different angles.
• Euler’s Formula: F+V-E = 2, where F, V, and E are the respective faces, vertices, and edges of polyhedra.

Important Questions for Class 8 Maths NCERT Solutions Chapter 10

NCERT Solutions for Class 8 Maths Video Chapter 10

FAQs on NCERT Solutions Class 8 Maths Chapter 10

Why are ncert solutions class 8 maths chapter 10 important.

We observe objects of various forms all around us in our daily lives, whether it's the house we live in or the objects that we use like a tumbler for drinking water. Hence, it is important to understand these shapes in detail so that when the need arises we are able to calculate the area and volume respectively, which is only possible if we understand the objects in 2D and 3D space. The NCERT Solutions Class 8 Maths Chapter 10 plays a vital role in explaining the same to the students so that they get a detailed understanding of the shapes as well as the combination of figures in both 2D and 3D perspectives.

Do I Need to Practice all Questions Provided in NCERT Solutions Class 8 Maths Visualising Solid Shapes?

The NCERT Solutions Class 8 Maths Visualising Solid Shapes has utilized a lot of neatly drawn diagrams and visually appealing charts, along with thoughtfully curated examples as well as exercise questions. The more the students will practice the same, the better they will get in observing the shapes, thereby improving their geometry skills. Hence, it is advisable for the students to practice all the questions given in the textbook.

What are the Important Topics Covered in NCERT Solutions Class 8 Maths Chapter 10?

The NCERT Solutions Class 8 Maths Chapter 10 starts with the introduction of two-dimensional and three-dimensional spaces, and how the objects differ in the view in both 2D and 3D. Furthermore, the concept of a map is discussed, moving on to the introduction of the polyhedron, its types, and Euler’s formula. Kids need to give an ample amount of time to each topic for building a solid foundation as it will be used in higher classes.

How Many Questions are there in Class 8 Maths NCERT Solutions Chapter 10 Visualising Solid Shapes?

There are a total of 16 questions in the NCERT Solutions Class 8 Maths Chapter 10 Visualising Solid Shapes. The students will find 10 to be very easy as they are of short answer type, 2 are moderately easy while 4 are a bit longer due to the drawing part involved in them. These problems are divided into two exemplar exercises.

How CBSE Students can utilize NCERT Solutions Class 8 Maths Chapter 10 effectively?

There are a lot of examples and exercises in the chapter to help the students understand the visualization of solids in 2D and 3D space. Hence, the entire lesson must be read carefully because each line includes important explanations and facts. In order to utilize the NCERT Solutions Class 8 Maths Chapter 10 effectively, the students must practice the examples to gain clear knowledge about the various shapes or objects, which will help them develop the appropriate problem-solving strategies and skills.

Why Should I Practice Class 8 Maths NCERT Solutions Visualising Solid Shapes Chapter 10?

The NCERT Solutions Class 8 Maths Visualising Solid Shapes Chapter 10 is written by top experts in their domains, who have accumulated solid geometry information in a style that is easily understandable by everyone. In addition, the CBSE board strongly encourages the students to study from the NCERT books, making them a credible resource to practice and excel in geometry.

NCERT Solutions for Class 8 Maths Chapter 10 Visualising Solid Shapes

NCERT Solutions for Class 8 Maths Chapter 10 Visualising Solid Shapes are provided below. Our solutions covered each questions of the chapter and explains every concept with a clarified explanation. To score good marks in Class 8 Mathematics examination, it is advised to solve questions provided at the end of each chapter in the NCERT book.

NCERT Solutions for Class 8 Maths Chapter 10 Visualising Solid Shapes are prepared based on Class 8 NCERT syllabus, taking the types of questions asked in the NCERT textbook into consideration. Further, all the CBSE Class 8 Solutions Maths Chapter 10 are in accordance with the latest CBSE guidelines and marking schemes.

Class 8 Maths Chapter 10 Exercise 10.1 Solutions

Class 8 Maths Chapter 10 Exercise 10.2 Solutions

Class 8 Maths Chapter 10 Exercise 10.3 Solutions

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• NCERT Solutions
• NCERT Class 8
• NCERT 8 Maths
• Chapter 10: Visualizing Solid Shapes

NCERT Solutions for Class 8 Maths Chapter 10 Visualising Solid Shapes

Ncert solutions class 8 maths chapter 10 – free pdf download.

NCERT Solutions for Class 8 Maths Chapter 10 Visualising Solid Shapes is provided in this article to assist the students of Class 8 in their studies. Are you looking for help in finding the answers to NCERT textbook questions for Visualising Solid Shapes? If yes, you are at the right place. NCERT Solutions is a very important resource for students of Class 8 under CBSE. The solutions for Class 8 CBSE Maths are based on the latest syllabus provided by the Board and have detailed explanations for all the questions provided in the NCERT textbooks. Get all exercise-wise NCERT Class 8 Maths Chapter 10 Solutions for students to boost their exam preparations and score good marks.

Access Answers to NCERT Class 8 Maths Chapter 10 Visualising Solid Shapes

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Exercise 10.1 Page No: 157

1. For each of the given solids, two views are given. Match for each solid the corresponding top and front views. The first one is done for you.

(a) (iii) (iv)

(b) (i) (v)

(c) (iv) (ii)

(d) (v) (iii)

(e) (ii) (i)

2. For each of the given solids, the three views are given. Identify for each solid the corresponding top, front and side views.

(a) (i) Front (ii) Side (iii) Top view

(b) (i) Side (ii) Front (iii) Top view

(c) (i) Front (ii) Side (iii) Top view

(d) (i) Front (ii) Side (iii) Top view

3. For each given solid, identify the top view, front view and side view.

(a) (i) Top view (ii) Front view (iii) Side view

(b) (i) Side view (ii) Front view (iii) Top view

(c) (i) Top view (ii) Side view (iii) Front view

(d) (i) Side view (ii) Front View (iii) Top view

(e) (i) Front view (ii) Top view (iii) Side view

4. Draw the front view, side view and top view of the given objects:

Exercise 10.2 Page No. 157

1. Look at the given map of a city.

Answer the following:

Colour the map as follows: Blue – water, red – fire station, orange – library, yellow – schools, green – park, pink – college, purple – hospital, brown – cemetery.

(a) Mark a green ‘X’ at the intersection of Road C and Nehru Road, Green ‘Y’ at the intersection of Gandhi Road and Road A.

(b) In red, draw a short street route from the library to the bus depot.

(c) Which is the further east, the city park or the market?

(d) Which is further south, the Primary School or the Sr. Secondary School?

(c) City Park

(d) Sr. Secondary School

2. Draw a map of your classroom using proper scales and symbols for different objects.

It can be anything. For your reference, we have shared one classroom picture:

3. Draw a map of your school compound using proper scale and symbols for various features like a playground, main building, garden etc.

Do it yourself

4. Draw a map giving instructions to your friend so that she reaches your house without any difficulty.

Exercise 10.3 Page No. 166

1. Can a polyhedron have for its faces:

(i) 3 Triangles?

(ii) 4 triangles?

(iii) A square and four triangles?

(i) No, such polyhedrons are not possible. A polyhedron should have a minimum of 4 faces.

(ii) Yes, a triangular pyramid has 4 triangular faces.

(iii) Yes, as a square pyramid has a square face and 4 triangular faces.

2. Is it possible to have a polyhedron with any given number of faces? (Hint: Think of a pyramid)

It is possible only if the number of faces is greater than or equal to 4.

3. Which are prisms among the following:

(i) A nail: It is not a prism.

(ii) Unsharpened pencil: It is a prism.

(iii) A table weight: It is not a prism.

(iv) A box: It is a prism.

4. (i) How are prisms and cylinders alike?

(ii) How are pyramids and cones alike?

(i) A cylinder can look like a circular prism, a prism with a circular base.

(ii) A cone can be a circular pyramid, a pyramid with a circular base.

5. Is a square prism the same as a cube? Explain.

Yes, a square prism can also be a cube. A square prism has a square as its base. However, its height is not necessarily the same as the side of the square. Thus, a square prism can also be a cuboid.

6. Verify Euler’s formula for the given solids.

(i) Number of faces, F = 7

Number of edges, E = 15

Number of vertices, V = 10

As per formula, F + V – E = 2

Substitute the values, we have

F + V – E = 7 + 10 – 15

Hence, verified.

(ii) Here, F = 9, V = 9 and E = 16

Using formula, F+ V – E = 2

F + V – E = 9 + 9 – 16 = 2

Hence, Euler’s formula is verified.

7. Using Euler’s formula, find the unknown:

Euler’s formula: F + V – E = 2

Where, F = Faces, V = Vertices and E = Edges

(i) F + 6 – 12 = 2

(ii) 5 + V – 9 = 2

V – 4 = 2

⇒ V = 4 + 2

(iii) 20 + 12 – E = 2

32 – E = 2

⇒ E = 32 – 2

8. Can a polyhedron have 10 faces, 20 edges and 15 vertices?

From the given data, we have

Every polyhedron satisfies Euler’s formula, which is stated as, F + V – E = 2

For the given polygon,

F + V – E = 10 + 15 – 20 = 25 – 20 = 5, which is not equal to 2.

Therefore, a polyhedron cannot have 10 faces, 20 edges and 15 vertices , as Euler’s formula is not satisfied.

NCERT Solutions for Class 8 CBSE Maths Chapter 10 introduces the different dimensions of shapes and geometrical figures to the students. This chapter contains some very interesting concepts, such as visualising solid shapes and views of 3D-shapes like cubes, cylinders, cones, spheres, etc., mapping space around us and faces, edges and vertices. NCERT Solutions Class 8 Chapter 10 Visualising Solid Shapes chapter is very interesting and easy to understand.

NCERT Solutions for Class 8 Maths Chapter 10 Exercises:

Get detailed solutions for all the questions listed under the below exercises: Exercise 10.1 Solutions : 4 Questions (Short answers) Exercise 10.2 Solutions : 4 Questions (3 Short answers, 1 Long answer) Exercise 10.3 Solutions : 8 Questions (Short answers)

NCERT Solutions for Class 8 Maths Chapter 10 is mainly about recognising 2D and 3D objects and different shapes in nested objects, maps and verification of polyhedrons. The solutions to all the topics in Chapter 10 are covered in a detailed and easy-to-understand way. The main topics covered in this chapter include the following:

Key Features of NCERT Solutions for Class 8 Maths Chapter 10 Visualising Solid Shapes

• Easy and simple techniques are used to find accurate solutions.
• These solutions are designed based on the latest syllabus.
• Solutions are prepared by subject experts.
• NCERT Solutions helps students by providing detailed explanations in a stepwise manner.
• NCERT Solutions are helpful for the preparation of competitive exams.

Disclaimer:

Dropped Topics – 10.1 Introduction, 10.2 Views of 3D-Shapes, 10.3 Mapping Space Around Us and 10.4 Faces, Edges and Vertices.

Frequently Asked Questions on NCERT Solutions for Class 8 Maths Chapter 10

List out the frequently asked topics of chapter 10 of ncert solutions in the board exam of class 8 maths., are ncert solutions for class 8 maths chapter 10 important from an exam point of view, why should students download ncert solutions for class 8 maths chapter 10 from byju’s, leave a comment cancel reply.

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Home » 8th Class » NCERT Exemplar Class 8 Maths Unit 6 Visualising Solid Shapes

NCERT Exemplar Class 8 Maths Unit 6 Visualising Solid Shapes

Candidates can download NCERT Exemplar Class 8 Maths Unit 6 from this page. The exemplar has been provided by the National Council of Educational Research & Training (NCERT) and the candidates can check it from below for free of cost. It contains objective, very short answer type, short answer type, and long answer type questions. Along with it, the answer for each question has also been provided. From the NCERT Exemplar Class 8 Maths Unit 6, candidates can understand the level and type of questions that are asked in the exam. 

NCERT Class 8 Maths Unit 6 is for Visualising Solid Shapes. The type of questions that will be asked from NCERT Class 8 Maths Unit 6 are displayed in the below provided NCERT Exemplar Class 8 Maths Unit 6. With the help of it, candidates can prepare well for the examination.

Also Check: NCERT Solutions for Class 8 Maths

• 3D shapes/objects are those which do not lie completely in a plane.
• 3D objects have different views from different positions.
• A solid is a polyhedron if it is made up of only polygonal faces, the faces meet at edges which are line segments and the edges meet at a point called vertex.
• Euler’s formula for any polyhedron is, F + V – E = 2. Where F stands for number of faces, V for number of vertices and E for number of edges.
• Types of polyhedrons:

(1) and (2) are convex polyhedrons whereas

(3) and (4) are non convex polyhedron.

• Regular polyhedra or platonic solids: A polyhedron is regular if its faces are congruent regular polygons and the same number of faces meet at each vertex. For example, a cube is a platonic solid because all six of its faces are congruent squares. There are five such solids– tetrahedron, cube, octahedron, dodecahedron and icosahedron. e.g.

• A prism is a polyhedron whose bottom and top faces (known as bases) are congruent polygons and faces known as lateral faces are parallelograms (when the side faces are rectangles, the shape is known as right prism).
• A pyramid is a polyhedron whose base is a polygon and lateral faces are triangles.
• A map depicts the location of a particular object/place in relation to other objects/places.

• Scale is the relationship between the drawing’s/model’s dimensions to the actual object’s dimensions.
• In a map, symbols are used to depict the different objects and places
• Maps involve a scale which is fixed for a particular map.

Think and Discuss

• Explain how you would find the surface area of an open-top box that is shaped like a rectangular prism.
• Describe the shapes in a net used to cover a cylinder.

Solved Examples

In examples 1 and 2, write the correct answer from the given four options.

In examples 3 and 4, fill in the blanks to make the statements true

Multiple Choice Questions

Fill in the Blanks Type Questions

True False Type Questions

Short Answer Type Questions

Activity 1: Find the most appropriate way to reach from start to finish. (Use a coloured pen of your choice to show the path traced.)

Activity 2: Rohit is a 7 year old young boy. His uncle Raj asked him to draw a map to reach Sport’s Complex from his (Rohit’s) house. He drew the following map.

Activity 3: Look at the map of city given on the next page:

(a) Colour the map using the given colour code as follows. Blue-water, Red-Fire station, White-Hospital, GreenParks, Cream-River Bed, Brown-Mountains.

(b) Mark the shortest route from House to Pool with the help of arrowes.

(c) Put X at the intersection of Chatra Marg and House Lane.

Activity 4: Draw the nets given below on coloured sheets by taking each side of the triangle as 3cm, and try to form the shapes shown in front of it. Count the number of edges, faces and vertices in ends and verify the Euler’s formula.

Activity 5: Guess who am I? My name is given in the box below. Oops! Spelling of my name is jumbled up. Try to identify it from the clues given below and write it in the blank space.

(1) I am a polyhedron with least number of faces. ________

(2) I am a prism whose all faces are square. ________

(3) Looks like marbles but have no vertex. ________

(4) I am a solid whose base is polygonal and other faces are triangles. ________

Activity 6: Draw the map of your locality, showing the details of your sector/ block. Also highlight the appropriate landmarks which will help your friend to locate your house in your sector/block.

Activity 7: Crossword Puzzle

Answer the following based on the hints given below.

1. Polyhedron whose lateral faces are parallelograms.

2. Prism having fifteen edges.

5. Another name for a square prism.

7. Polyhedron made up of four triangles.

9. Polyhedron made up of convex polygons.

2. Polyhedron whose lateral faces are triangles.

3. In a solid shape, the line segment joining two vertices not lying on the same face.

4. A 3-D shape having no vertex.

6. A solid figure having only one vertex.

7. Number of pentagons in a pentagonal prism.

10. Point where edges of a solid shape meet.

Click here to downlod the NCERT Exemplar Class 8 Maths Unit 6 Visualising Solid Shapes

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Revision Notes on Visualizing Solid Shapes

Two-dimensional shapes.

Plane figures with only two measurements –length and width are called 2-D shapes.

Three-dimensional shapes

Solid figures with three measurements –length, width and height are called 3D shapes.

Views of 3D-Shapes

As the 3-D shapes are solid in nature so they may have a different view from different sides.

When we draw the top view, front view and side view on paper then it will look like this.

Draw the front view, side view and the top view of the given figure.

Mapping Space around Us

A map shows the location of a particular thing with respect to others.

Some important points related to map:

To represent different objects or place different symbols are used.

A map represents everything proportional to their actual size not on the basis of perspective. It means that the size of the object will remain the same irrespective of the observer’s viewpoint.

 A particular scale is used to draw a map so that the lengths drawn are proportional with respect to the size of the original figures.

This is the map which shows the different routes from Nehru road.

Faces, Edges and Vertices

Faces  – All the flat surfaces of the three 3-D shapes are the faces. Solid shapes are made up of these plane figures called faces.

Edges – The line segments which make the structure of the solid shapes are called edges. The two faces meet at the edges of the 3D shapes.

Vertex – The corner of the solid shapes is called vertex. The two edges meet at the vertex. The plural of the vertex is vertices.

Polyhedrons

Polygons are the flat surface made up of line segments. The 3-D shapes made up of polygons are called polyhedron.

These solid shapes have faces, edges and vertices.

The polygons are the faces of the solid shape.

Three or more edges meet at a point to form a vertex.

The plural of word polyhedron is polyhedral.

Non-polyhedron

The solid shape who’s all the faces are not polygon are called non-polyhedron. i.e. it has one of the curved faces.

Convex Polyhedrons

If the line segment formed by joining any two vertices of the polyhedron lies inside the figure then it is said to be a convex polyhedron.

Non-convex or Concave Polyhedron

If anyone or more line segments formed by joining any two vertices of the polyhedron lie outside the figure then it is said to be a non-convex polyhedron.

Regular Polyhedron

If all the faces of a polyhedron are regular polygons and its same number of faces meets at each vertex then it is called regular polyhedron.

Non-regular Polyhedron

The polyhedron which is not regular is called non-regular polyhedron. Its vertices are not made by the same number of faces.

In this figure, 4 faces meet at the top point and 3 faces meet at all the bottom points.

If the top and bottom of a polyhedron are a congruent polygon and its lateral faces are parallelogram in shape, then it is said to be a prism.

If the base of a polyhedron is the polygon and its lateral faces are triangular in shape with a common vertex, then it is said to be a pyramid.

Number of faces, vertices and edges of some polyhedrons

Euler’s formula

Euler’s formula shows the relationship between edges, faces and vertices of a polyhedron.

Every polyhedron will satisfy the criterion F + V – E = 2,

Where F is the number of faces of the polyhedron, V is the vertices of the polyhedron and E is the number of edges of the polyhedron.

Using Euler's formula, find the number of faces if the number of vertices is 6 and the number of edges is 12.

Given, V = 6 and E = 12.

We know Euler’s formula, F + V – E = 2

So, F + 6 – 12 = 2.

Hence, F = 8.

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8th Class Mathematics Visualising Solid Shapes Question Bank

Done visualising solid shapes total questions - 20.

question_answer 1) Which of the following is NOT a polyhedron?

question_answer 3) Which of the following is NOT a three dimensional shape?

A)  Square prism done clear

B)           Sphere done clear

C)           Triangular pyramid done clear

D)           Circle done clear

question_answer 4) Euler's formula for any polyhedron, where F stands for the number of faces, V stands for the number of vertices and E stands for the number of edges is __.

A)  \[\text{F+V+E=2}\] done clear

B)           \[\text{F-V+E=2}\]   done clear

C)           \[\text{F+V-E=2}\]               done clear

D)           \[\text{F-V-E=2}\]     done clear

question_answer 5) Which of the following is the net of a cone?

A)  9        done clear

B)           10       done clear

C)           8            done clear

D)           6         done clear

question_answer 7) Which of the following CANNOT be true for polyhedron?

A)  Faces = 4, Vertices = 4, Edges = 6 done clear

B)           Faces = 8, Vertices = 6, Edges = 12 done clear

C)           Faces = 5, Vertices = 1, Edges = 8 done clear

D)           Faces = 20, Vertices = 12, Edges = 30 done clear

question_answer 8) Which of the following is the net of a hexagonal prism?

D)           None of these  done clear

question_answer 9) The number of faces in a square prism is

A)  4                                 done clear

B)           6         done clear

C)           8                                 done clear

question_answer 10) Number of faces, vertices and edges in the square pyramid are respectively______.

A)  4, 6, 12                       done clear

B)           7, 5, 10           done clear

C)           5, 5, 8             done clear

D)           4, 4, 6 done clear

question_answer 12) Solid having only line segments as its edges is a ______.

A)  Polyhedron                 done clear

B)           Cone   done clear

C)           Cylinder                      done clear

D)           Polygon           done clear

question_answer 13) If a polyhedron has 12 vertices and 8 faces, then the number of edges of the polyhedron is ____.

A)  12                               done clear

B)           14       done clear

C)           16                               done clear

D)           18       done clear

question_answer 14) Number of edges in a triangular prism is

A)  9                                 done clear

C)           5                                 done clear

D)           8         done clear

question_answer 15) Which of the following will not form a polyhedron?

A)  1 square and 4 triangles done clear

B)           2 triangles and 3 rectangles done clear

C)           3 triangles done clear

D)  1 pentagon and 5 triangles done clear

A)  8, 6, 24, 54                 done clear

B)           8, 6, 56, 22     done clear

C)           6, 8, 24, 54                 done clear

D)           7, 8, 56, 22 done clear

A)   P\[\to \] (ii); Q\[\to \](iv); R\[\to \](i); S\[\to \](iii) done clear

B)           P\[\to \](iv); Q\[\to \](i); R\[\to \](ii); S\[\to \](iii) done clear

C)           P\[\to \](i); Q\[\to \](ii); R\[\to \](iii); S\[\to \](iv) done clear

D)           P\[\to \](iii); Q\[\to \](i); R\[\to \](ii); S\[\to \](iv) done clear

question_answer 18) Select the INCORRECT match.

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NCERT solutions for Mathematics Class 8 chapter 10 - Visualising Solid Shapes [Latest edition]

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Solutions for chapter 10: visualising solid shapes.

Below listed, you can find solutions for Chapter 10 of CBSE NCERT for Mathematics Class 8.

NCERT solutions for Mathematics Class 8 Chapter 10 Visualising Solid Shapes Exercise 10.1 [Pages 157 - 160]

For each of the given solid, the two views are given. Match for each solid the corresponding top and front views.

For the given solid, the three views are given. Identify for each solid the corresponding top, front and side views.

For the given solid, identify the top view, front view and side view.

Draw the front view, side view and top view of the given objects.

A military tent

A hexagonal block

NCERT solutions for Mathematics Class 8 Chapter 10 Visualising Solid Shapes Exercise 10.2 [Page 163]

Look at the given map of a city.

Answer the following.

(a) Colour the map as follows: Blue − water plant, red − fire station, orange − library, yellow − schools, green − park, pink − college, purple − hospital, brown − cemetery.

(b) Mark a green ‘X’ at the intersection of Road ‘C’ and Nehru Road, Green ‘Y’ at the intersection of Gandhi Road and Road A.

(c) In red, draw a short street route from library to the bus depot.

(d) Which is further east, the city park or the market?

(e) Which is further south, the Primary School or the Sr. Secondary School?

Draw a map of your class room using proper scale and symbols for different objects.

Draw a map of your school compound using proper scale and symbols for various features like play ground main building, garden etc.

Draw a map giving instructions to your friend so that she reaches your house without any difficulty.

NCERT solutions for Mathematics Class 8 Chapter 10 Visualising Solid Shapes Exercise 10.3 [Pages 166 - 167]

Can a polyhedron have for its faces 3 triangles?

Can a polyhedron have for its faces 4 triangles?

Can a polyhedron have for its faces a square and four triangles?

Is it possible to have a polyhedron with any given number of faces? ( Hint:  Think of a pyramid).

The given Figure are prisms or not?

How are prisms and cylinders alike?

How are pyramids and cones alike?

Is a square prism same as a cube? Explain.

Verify Euler’s formula for given solids

Verify Euler’s formula for given solids.

Using Euler’s formula, find the unknown.

Can a polyhedron have 10 faces, 20 edges and 15 vertices?

NCERT solutions for Mathematics Class 8 chapter 10 - Visualising Solid Shapes

Shaalaa.com has the CBSE Mathematics Mathematics Class 8 CBSE solutions in a manner that help students grasp basic concepts better and faster. The detailed, step-by-step solutions will help you understand the concepts better and clarify any confusion. NCERT solutions for Mathematics Mathematics Class 8 CBSE 10 (Visualising Solid Shapes) include all questions with answers and detailed explanations. This will clear students' doubts about questions and improve their application skills while preparing for board exams.

Further, we at Shaalaa.com provide such solutions so students can prepare for written exams. NCERT textbook solutions can be a core help for self-study and provide excellent self-help guidance for students.

Concepts covered in Mathematics Class 8 chapter 10 Visualising Solid Shapes are Viewing Different Sections of a Solid, Mapping Space Around Us, Faces, Edges and Vertices, Plane Figures and Solid Shapes, Nets for Building 3-d Shapes - Cube, Cuboids, Cylinders, Cones, Pyramid, and Prism, Concept of Polyhedron, Prism, Concept of Pyramid, Euler's Formula.

Using NCERT Mathematics Class 8 solutions Visualising Solid Shapes exercise by students is an easy way to prepare for the exams, as they involve solutions arranged chapter-wise and also page-wise. The questions involved in NCERT Solutions are essential questions that can be asked in the final exam. Maximum CBSE Mathematics Class 8 students prefer NCERT Textbook Solutions to score more in exams.

Get the free view of Chapter 10, Visualising Solid Shapes Mathematics Class 8 additional questions for Mathematics Mathematics Class 8 CBSE, and you can use Shaalaa.com to keep it handy for your exam preparation.

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CBSE Class 8 Maths Revision Notes Chapter 10

Home » CBSE » CBSE Class 8 Maths Revision Notes Chapter 10

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CBSE Class 8 Mathematics Revision Notes Chapter 10 – Visualising Solid Shapes

Revision notes for cbse class 8 mathematics chapter 10 – free pdf download, download revision notes class 8 mathematics chapter 10 – free pdf.

In these Class 8 Mathematics Chapter 10 Notes , students will learn about visualising solid shapes. In addition, in these Class 8 Chapter 10 Mathematics Notes , students will get to know the significant details of the chapter that are important for their final examination. Along with Chapter 10 Mathematics Class 8 Notes , Extramarks will provide students with essential questions for quick and instant preparation. Moreover, Class 8 Mathematics Notes Chapter 10 will be a student’s last-minute revision guide, providing all the necessary information. These notes are based on the CBSE Syllabus. 

There are Three Different Kinds of Shapes

In this part of Class 8 Mathematics Chapter 10 Notes , students will learn about different shapes.

• One-dimensional shapes: These are shapes with only length as a dimension. Think about the following illustration—a line.
• Two-dimensional shapes :  Two-dimensional shapes have length and breadth as their two dimensions. Shapes include things like rectangles, triangles, and polygons. The term “2D figures” is often used to describe two-dimensional objects.
• Three-dimensional shapes: Three-dimensional shapes are solid objects and shapes that have length, breadth, height, and depth. Examples of geometric shapes include cubes, cylinders, cones, cuboids, spheres, and others.
• Faces: A flat or curved surface on a three-dimensional figure is known as a face.
• Edges: Two faces of a solid are connected by a line segment known as an edge.
• Polyhedron: Polyhedron refers to a three-dimensional figure with polygonal faces. 
• Prism: It is a polyhedron with parallelograms on the lateral faces and congruent polygons on the bottom and top faces (referred to as bases). The shape is referred to as a right prism when the side faces are rectangles.
• Pyramid: It is a polyhedron with a polygon base and triangle lateral sides.
• A place on a graph on which three or more edges converge is known as a vertex.
• Base: The face on which a polyhedron is named is its base.
• Euler’s formula for any polyhedron is F+V−E=2, where F is the number of faces, V is the number of vertices, and E is the number of edges.
• Object recognition in 2D and 3D.
• Views of a 3D object may differ based on their position.
• Mapping means where one object or place is in relation to other objects or places.
• Symbols are used to denote various objects and locations on a map.
• There is no reference or viewpoint on a map.
• The scale of a map is predetermined for each map.  
• Convex means any two points on a polyhedron’s surface that can be connected by a line segment that is entirely inside or on the polyhedron, such as the cube, cuboid, tetrahedron, pyramid, and prism.

A Quick Overview Of Class 8 Mathematics Chapter 10 Visualising Solid Shapes

Students will learn about visualising solid shapes, views of three-dimensional shapes, mapping our surroundings, and the faces, edges, and vertices of three-dimensional shapes in these Class 8 Mathematics Chapter 10 Notes . Let us now discuss the topics and subtopics covered in this chapter.

Ex.10.1 – Introduction to the Chapter

You must have studied different solid and plane shapes in your previous classes.   Because they only have two measurements, length, and breadth, plane shapes are also referred to as two-dimensional shapes. In contrast, solid shapes are referred to as three-dimensional shapes because they have three dimensions—length, breadth, and height. The solid shapes also take up some room. 2-D and 3-D figures are also referred to as two-dimensional and three-dimensional shapes, respectively.

Ex.10.2 – View Of 3D-Shapes

You will gain knowledge about the views of various three-dimensional shapes, such as cones, cylinders, cubes, spheres, etc., in this section. You will learn that three-dimensional objects can be drawn from a perspective as they look different from different positions. You will discover that 3-D shapes have a front, top, and side view. Some real-life examples are given to help you understand the concept clearly.

Ex. 10.3 –  Mapping Around Us

You have been using maps in your previous classes. You must have been asked to mark rivers, mountains, states, countries, cities, etc., on a map by your geography teachers. Your history teachers must have asked you to find a specific location where a certain event had taken place in the past.

You will learn how to read maps in this section. What conclusions and concepts can you draw from studying maps? What information do they provide, and what information do they not provide?

Ex.10.3 – Faces, Edges, And Vertices

In this part, you will learn about the faces, edges, and vertices of three-dimensional shapes. You will also understand the total number of edges, faces, and vertices different 3-D shapes include.

To successfully answer questions based on various solid and plane shapes, students should have a thorough understanding of these concepts.

Download our most recent Class 8 Mathematics Chapter 10 Revision Notes Free PDF right away to get a thorough explanation of Chapter 10 Visualising Solid Shapes . Extramarks subject specialists will clarify any questions about various solid and plane shapes and assist you in understanding the fundamental concepts of the chapter. These notes contain all the topics in the NCERT Books concisely. Download the Class 8 Mathematics Chapter 10 Notes on this page to improve your exam results. Once you go through these notes, you can easily solve CBSE Sample Papers to test your understanding. These notes also contain CBSE Extra Questions that will help students test their understanding.

Key Benefits Of Mathematics Class 8 Visualising Solid Shapes Notes

Visualising Solid Shapes Class 8 Notes by Extramarks include clear and student-friendly writing that will make it easier for you to understand the chapter’s concepts. Because of how well these revision notes work, you will truly understand every subject. You will be able to answer all the numerical questions from the chapter that were asked on the exam because you will accurately remember all the concepts. You could revise the key concepts and formulas from the chapter quickly before the exams using these Visualising Solid Shapes Notes.

Some of the main benefits of the Mathematics Class 8 Visualising Solid Shapes notes are discussed below.

• The students can quickly review and practice the chapter’s concepts using the Class 8 Chapter 8 Notes.
• Visualising Solid Shapes notes include all the crucial formulas and chapter topics, which will help you save a lot of time.
• These notes were written after thorough research by subject matter experts with many years of teaching experience.
• The notes for Mathematics Class 8: Visualising Solid Shapes provide several key suggestions for correctly resolving the chapter’s challenging numerical problems.
• Free Visualising Solid Shapes Class 8 Notes in PDF are available for students to download and can be accessed online and offline at their convenience.

These CBSE Revision Notes are made according to the CBSE Syllabus . The questions in these notes are based on CBSE Past Years’ Question Papers. These notes contain Important Questions and Formulas to help students achieve better marks in their examinations.   

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FAQs (Frequently Asked Questions)

1. find the number of vertices of hexagonal prisms..

Number of vertices = 2 × Number of sides = 2 × 6 = 12

2. What is Euler’s formula for polyhedron?

According to Euler’s polyhedron formula, any solid shape will always equal 2 when the number of vertices (V) is subtracted from the number of edges (E) and added to the number of faces (F).

So, V – E + F = 2

3. What will be the minimum number of planes required to form a solid?

At least four planes are required to form a solid. The solid formed using only four planes is called a tetrahedron or a triangular pyramid.

4. What do you mean by polyhedron?

It refers to a three-dimensional figure with polygonal faces.

5. What do you mean by one-dimensional figure?

A one-dimensional figure means shapes with only length as a dimension.  

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NCERT Exemplar Class 8 Maths Chapter 6 Visualising Solid Shapes

June 21, 2022 by Sastry CBSE

NCERT Exemplar Class 8 Maths Chapter 6 Visualising Solid Shapes are part of NCERT Exemplar Class 8 Maths . Here we have given NCERT Exemplar Class 8 Maths Chapter 6 Visualising Solid Shapes.

Question. 2 Which of the following will not form a polyhedron? (a) 3 triangles (b) 2 triangles and 3 parallelograms (c) 8 triangles (d) 1 pentagon and 5 triangles Solution. (a) A polyhedron is bounded by more than four polygonal faces. But in case of 3 triangles, it is not possible. So, option (a) does not form a polyhedron.

Question. 3 Which of the following is a regular polyhedron? (a) Cuboid (b) Triangular prism (c) Cube (d) Square prism Solution. (c) A polyhedron is regular, if its faces are congruent regular polygons and the same number of faces meet at each vertex. Hence, a cube satisfies- all the properties for a regular polyhedron.

Question. 4 Which of the following is a two dimensional figure? (a) Rectangle              (b) Rectangle prism (c) Square pyramid (d) Square prism Solution. (a) A two dimensional figure have two dimensions (measurements) like length and breadth. In the given options, only rectangle has two dimensions, i.e. length and breadth.

Question. 5 Which of the following can be the base of a pyramid? (a) Line segment (b) Circle (c) Octagon (d) Oval Solution. (c) Since, a pyramid is a polyhedron whose base is a polygon and lateral faces are triangles. Hence, octagon can be the base of a pyramid.

Question. 6 Which of the following 3-D shapes does not have a vertex? (a) Pyramid (b) Prism (c) Cone (d) Sphere Solution. (d) As we kndw that, a vertex is a meeting point of two or more edges. Since, a sphere has only one curved face, so it has no vertex and no edges.

Question. 7 Solid having only line segments as its edges is a (a) Polyhedron (b) Cone (c) Cylinder (d) Polygon Solution. (a) In polyhedron, the faces meet at edges which are line segments and edges meet at vertex. –

Question. 13 We have 4 congruent equilateral triangles. What do we need more to make a pyramid? (a) An equilateral triangle. (b) A square with same side length as of triangle. (c) 2 equilateral triangles with side length same as triangle. (d) 2 squares with side length same as triangle. Solution. (b) We know that, a pyramid is a polyhedron, whose base is a polygon and lateral faces are triangles. But in the question, we have only 4 congruent equilateral triangles. Thus, we have to add a polygon in the base of atleast a four-sided figure. Hence, option (b) is required to make a pyramid.

Fill in the Blanks In questions 22 to 41, fill in the blanks to make the statements true.

Question. 22 Square prism is also called a______ Solution. Square prism is called a cube. We know that, a square prism has a square base, a congruent square top and the sides are parallelograms. So, it is also a cube.

Question. 25 A pyramid on an n sided polygon has______faces. Solution. A pyramid on an n sided polygon has n + 1 faces. We know that, in a pyramid, the number of faces is 1 more than the number of sides of the polygohal base.

Question. 28 A solid figure with only 1 vertex is a______ Solution. A solid figure, with only 1 vertex is a cone. We know that, cone is a solid figure which has a circular base and its all other surfaces comes to a point called vertex.

Question. 31 In a three-dimensional shape, diagonal is a line segment that joins two vertices that do not lie on the______face. Solution. In a three-dimensional shape, diagonal is a line segment that joins two vertices that do not lie on the same face.

Question. 32 If 4 km on a map is represented by 1 cm, then 16 km is represented by______cm. Solution. Given, 4 km on a map is represented by 1 cm, then 1 km on a map is represented by 1/4 cm. Hence, 16 km on a map is represented by – x 16 = 4 cm

Question. 35 If a pyramid has a hexagonal base, then the number of vertices is______ Solution. If a pyramid has a hexagonal base, then the number of vertices is 7. We know that, in a pyramid the number of vertices is 1 more than the number of sides of the polygonal base.

Question. 39 Total number of regular polyhedron is______ Solution. Total number of regular polyhedron is five, i.e. cube, octahedron, tetrahedron, dodecahedron and icosahedron.

Question. 40 A regular polyhedron is a solid made up of______faces. Solution. A regular polyhedron is a solid made up of congruent faces. [according to the definition of regular polyhedron]

True/False In questions 42 to 61, state whether the following statements are True or False.

Question. 42 The other name of cuboid is tetrahedron. Solution. False The other name of cuboid is rectangular prism.

Question. 43 A polyhedron can have 4 faces. Solution. False A polyhedron can have atleast 4 faces.

Question. 45 Regular octahedron has 8 congruent faces which are isosceles triangles. Solution. False A regular octahedron is obtained by joining two congruent square pyramids such that the vertices of the two square pyramids coincide. It has eight congruent equilateral triangular faces.

Question. 46 Pentagonal prism has 5 pentagons. Solution. False Pentagonal prism has 2 pentagons, one on the top and other on the base.

Question. 47 Every cylinder has 2 opposite faces as congruent circles, so it is also a prism. Solution. False The cylinder has a congruent cross-section which is a circle, so it could be called as a circular prism.

Question. 48 Euler’s formula is true for all three-dimensional shapes. Solution. False Euler’s formula is true only for polyhedrons, i.e. F+V-E = 2 Where F = faces, V = vertices and E = edges

Question. 52 Every, solid shape has a unique net. Solution. False A net is a flat figure that can be folded to form a closed, three-dimensional object. So, for an object, more than one net is possible but it is not true for the objects of all shapes.

Question. 53 Pyramids do not have a diagonal. Solution. True , Pyramids are polyhedron with a polygon as its base and other faces as triangles meeting at a common vertex and diagonal is a line joining the two opposite vertex. So, in pyramids, two opposite vertex cannot be formed. So, we can say pyramids has no diagonal.

Question. 55 A cuboid has atleast 4 diagonals. Solution. True In a cuboid, the number of diagonals is not least then 4.

Question. 56. All cubes are prism. Solution. True A cube is a prism because it has a square base, a congruent square top and the lateral sides are parallelograms.

Question. 57 A cylinder is a 3-D shape having two circular faces of different radii. Solution. False In a cylinder, the radii of the two circular faces are same. If the radii of two circular faces are different, then it will become frustum.

Question. 59 If a length of 100 m i% represented on a map by 1 cm, then the actual distance corresponding to 2 cm is 200 m. Solution. True When a length 100 m is respresented on a map by 1 cm. Then, actual distance corresponding to 2 cm = 2 x 100 = 200 m

Question. 66 How many edges does each of following solids have? (a) Cone    (b)Cylinder (c) Sphere (d)Octagonal Pyramid (e) Hexagonal Prism(f)Kaleidoscope Solution. (a) Cone has one edge. (b) Cylinder has two edges. (c) Sphere has no edge. (d) Octagonal pyramid has 16 edges. (e) Hexagonal prism has 18 edges. (f) Kaleidoscope has 9 edges. Note See edges in previous question’s solution figures.

Question. 86 How many faces, edges and vertices does a pyramid have with n sided polygon as its base? _ Solution. In a pyramid, the number of vertices is 1 more than the number of sides of the polygon base, i.e. vertices = n + 1 Also, the number of faces is 1 more than the number of sides of the polygonal base, i.e. faces = n+ 1 But the number of edges is 2 times the number of sides of the polygonal base, i.e. edges = 2 n .

NCERT Exemplar Solutions Class 8 Maths

• Chapter 1 Rational Numbers
• Chapter 2 Data Handling
• Chapter 3 Square-Square Root and Cube-Cube Root
• Chapter 4 Linear Equations in One Variable
• Chapter 5 Understanding Quadrilaterals and Practical Geometry
• Chapter 6 Visualising Solid Shapes
• Chapter 7 Algebraic Expressions, Identities and Factorisation
• Chapter 8 Exponents and Powers
• Chapter 9 Comparing Quantities
• Chapter 10 Direct and Inverse Proportion
• Chapter 11 Mensuration
• Chapter 12 Introduction to Graphs
• Chapter 13 Playing with Numbers

NCERT Exemplar Solutions

We hope the NCERT Exemplar Class 8 Maths Chapter 6 Visualising Solid Shapes help you. If you have any query regarding NCERT Exemplar Class 8 Maths Chapter 6 Visualising Solid Shapes, drop a comment below and we will get back to you at the earliest.

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NCERT Solutions

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Question 1:

For each of the given solid, the two views are given. Match for each solid the corresponding top and front views.

The given solids, matched to their respective side view and top view, are as follows.

Object Side view Top view

Page No 158:

Question 2:.

For each of the given solid, the three views are given. Identify for each solid the corresponding top, front and side views.

(i) Front (ii) Side (iii) Top

(i) Side (ii) Front (iii) Top

Page No 159:

Question 3:.

For each given solid, identify the top view, front view and side view.

(i) Top (ii) Front/Side (iii) Side/Front

(i) Top (ii) Side (iii) Front

(i) Front/Side (ii) Top (iii) Side/Front

Page No 160:

Question 4:.

Draw the front view, side view and top view of the given objects.

Page No 163:

Look at the given map of a city.

Answer the following.

(a) Colour the map as follows: Blue − water plant, red − fire station, orange − library, yellow − schools, green − park, pink − college, purple − hospital, brown − cemetery.

(b) Mark a green ‘X’ at the intersection of Road ‘C’ and Nehru Road, Green ‘Y’ at the intersection of Gandhi Road and Road A.

(c) In red, draw a short street route from library to the bus depot.

(d) Which is further east, the city park or the market?

(e) Which is further south, the Primary School or the Sr. Secondary School?

(a) The given map coloured in the required way is as follows.

(b)The marks can be put at the given points as follows.

(c) The shortest route from the library to bus depot is represented by red colour.

(d) Between the Market and the City Park, the City Park is further east.

(e) Between the Primary School and the Sr. Secondary School, the Sr. Secondary School is further south. ​​

Video Solution for Visualising Solid Shapes (Page: 163 , Q.No.: 1)

NCERT Solution for Class 8 math - Visualising Solid Shapes 163 , Question 1

Page No 166:

Can a polyhedron have for its faces

(i) 3 triangles? (ii) 4 triangles?

(iii) a square and four triangles?

(i) No, such a polyhedron is not possible. A polyhedron has minimum 4 faces.

(ii) Yes, a triangular pyramid has 4 triangular faces.

(iii) Yes, a square pyramid has a square face and 4 triangular faces.

Is it possible to have a polyhedron with any given number of faces? ( Hint: Think of a pyramid).

A polyhedron has a minimum of 4 faces.

Which are prisms among the following?

(i) It is not a polyhedron as it has a curved surface. Therefore, it will not be a prism also.

(ii) It is a prism.

(iii) It is not a prism. It is a pyramid.

(iv) It is a prism.

(i) How are prisms and cylinders alike?

(ii) How are pyramids and cones alike?

(i) A cylinder can be thought of as a circular prism i.e., a prism that has a circle as its base.

(ii) A cone can be thought of as a circular pyramid i.e., a pyramid that has a circle as its base.

Question 5:

Is a square prism same as a cube? Explain.

A square prism has a square as its base. However, its height is not necessarily same as the side of the square. Thus, a square prism can also be a cuboid.

Video Solution for Visualising Solid Shapes (Page: 166 , Q.No.: 5)

NCERT Solution for Class 8 math - Visualising Solid Shapes 166 , Question 5

Question 6:

Verify Euler’s formula for these solids.

(i) Number of faces = F = 7

Number of vertices = V = 10

Number of edges = E = 15

We have, F + V − E = 7 + 10 − 15 = 17 − 15 = 2

Hence, Euler’s formula is verified. ​(ii) Number of faces = F = 9

Number of vertices = V = 9

Number of edges = E = 16

F + V − E = 9 + 9 − 16 = 18 − 16 = 2

Hence, Euler’s formula is verified.

Video Solution for Visualising Solid Shapes (Page: 166 , Q.No.: 6)

NCERT Solution for Class 8 math - Visualising Solid Shapes 166 , Question 6

Page No 167:

Question 7:.

Using Euler’s formula, find the unknown.

By Euler’s formula, we have

F + V − E = 2

(i) F + 6 − 12 = 2

F − 6 = 2

(ii) 5 + V − 9 = 2

V − 4 = 2

(iii) 20 + 12 − E = 2

32 − E = 2

Thus, the table can be completed as

Video Solution for Visualising Solid Shapes (Page: 167 , Q.No.: 7)

NCERT Solution for Class 8 math - Visualising Solid Shapes 167 , Question 7

Question 8:

Can a polyhedron have 10 faces, 20 edges and 15 vertices?

Number of faces = F = 10

Number of edges = E = 20

Number of vertices = V = 15

Any polyhedron satisfies Euler’s Formula, according to which, F + V − E = 2

For the given polygon,

F + V − E = 10 + 15 − 20 = 25 − 20 = 5 ≠ 2

Since Euler’s formula is not satisfied, such a polyhedron is not possible.

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Visualising Solid Shapes Class 8 MCQ Test (Online Available)

Free mcq test, table of content, visualising solid shapes test - 24.

Duration: 10 Mins

Maximum Marks: 10

Read the following instructions carefully.

1. The test contains 10 total questions.

2. Each question has 4 options out of which only one is correct .

3. You have to finish the test in 10 minutes.

4. You will be awarded 1 mark for each correct answer.

5. You can view your Score & Rank after submitting the test.

6. Check detailed Solution with explanation after submitting the test.

7. Rank is calculated on the basis of Marks Scored & Time

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The chapter Visualising Solid Shapes is one of the important chapters in class 8. The highly qualified experts of Selfstudys developed these Visualising Solid Shapes class 8 MCQ to test what students have learnt and also helps them to identify their strengths and weaknesses. 

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• Time Management: The Visualising Solid Shapes class 8 MCQ helps the students to manage their time effectively. Time management reduces the chance of procrastination which can increase the chances for scoring well in the examination for all the students. As the time duration of the Visualising Solid Shapes class 8 MCQ will only be 10 minutes, it can be helpful for students as they will have more time for other important study materials. 
• Fast: The Visualising Solid Shapes history class 8 MCQ is fast as compared to other modes of exam available. Examples include offline (pen and paper) etc. This can be beneficial for students as they will get the status of their exam preparation fast. 
• Developed by the Subject Matter Experts: These Visualising Solid Shapes class 8 MCQ are developed by the subject matter experts of selfstudys.com who have years of experience in the educational field and are aware of the most common questions which can be asked in examinations. 
• Give the idea of the pattern of the exam: The Visualising Solid Shapes class 8 MCQ gives the idea of the pattern of the exam to the students which can make them confident and also help them to score well in the exam. 
• Improve the skills of the students: The Visualising Solid Shapes history class 8 MCQ can significantly improve critical thinking, management skills and time management skills. 

Hacks to Score Well in the Visualising Solid Shapes class 8 MCQ

If a student want to score well in the Visualising Solid Shapes class 8 MCQ, they can try the following hacks: 

• Read the complete question: It is advisable for students to read the entire question of the MCQ on Visualising Solid Shapes history class 8 completely as it helps them to understand the requirement of the question. Students often feel that they know the answer by looking at the question and without reading the complete question, they choose the most logical answer. This mistake is very common among the students. 
• Answer it in your mind first: Answer the question in your mind after reading the Visualising Solid Shapes history class 8 MCQ without looking at the options. Try to answer it without looking at the options as it will help you to be completely sure about the answer. 
• Attempt the questions you know first: Students are advised to attempt the questions for which they are completely sure that they know the answer whereas if a student doesn’t know the particular answer, they can skip it. By doing this, no unnecessary time will be wasted and time management will be ensured. 
• Make a guess: Students should make a guess while attempting the Visualising Solid Shapes class 8 MCQ because there is no negative marking. So, there is no need to skip any questions. 

How To Select The Correct Answers To The Visualising Solid Shapes History Class 8 MCQ?

• Use the process of elimination: After reading the entire questions and all the four options, students can use the process of elimination for the options for which they are 100% sure that they are incorrect. Even if they know the correct option, students are advised to use the elimination process. 
• “All of the above” and “None of the above”:  While attempting the Visualising Solid Shapes class 8 MCQ, if you see options like “All of the above” and “none of the above”, prefer not to choose them unless you are 100% sure as students think that this is the correct option.
• Find the answers hidden in the Question: A lot of times, the answers are hidden in the given questions so, try to find the answers hidden in Visualising Solid Shapes class 8 MCQ. Try decoding the questions by rereading them as you can find them in the questions itself. 
• True or False Test: Doing a true or false test in Visualising Solid Shapes Maths Class 8 MCQ can be very beneficial as it can be easier for a student to not consider all the false answer options and choose the correct answer.
• Possibility of two correct answers: If in case, two answers look correct with all of the above options while attempting the Class 8 Visualising Solid Shapes of History MCQ, then there is a strong possibility that it is the correct answer option. 

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NCERT Solutions for Visualizing Solid Shapes Exercise 10.1 Class 8 Maths

Exercise 10.1 Class 8 Maths: All CBSE Class 8 understudies can allude to this article for NCERT Solutions for Class 8 Science Chapter 10 – Reaching the Age of Adolescence. These arrangements will assist understudies with clearing the minutest of questions. Likewise, they will end up being the most accommodating assets while planning for end of the year tests. The best thing is that you can download these Class 8 Chapter 10 Science NCERT Solutions as a PDF to review disconnected.

Chapter 10, Visualizing Solid Shapes, incorporates a bunch of answers for every one of the inquiries gave in the NCERT course book practice 10.1. All arrangements are planned by specialists, as indicated by the most recent CBSE schedule and rules. This exercise assists understudies with understanding Views of 3D-Shapes where the student needs to distinguish every strong and their comparing parts view, for example, top and front perspectives, front and side perspectives and so on. Download NCERT Solutions for Maths Chapter 10 and practice without any interruptions.

Exercise 10.1 Class 8 Maths: An Overview

The tenth part of CBSE Class 8 Maths named ‘Visualising Solid Shapes’ is a significant point according to the test viewpoint. PDF of NCERT Class 8 Chapter 8 Solutions will assist understudies with understanding the right way to deal with and answer the inquiries fittingly. The answers for Class 8 CBSE Maths given here depend on the most recent prospectus given by the board and have definite clarifications for every one of the inquiries given in the NCERT course books.

NCERT Solutions for Exercise 10.1 Class 8 Maths: PDF Download

Students appearing for their Class 8 examinations need to ensure that they prepare every chapter thoroughly. The NCERT Solutions for Exercise 10.1 Class 8 Maths are easily available on the website. Since it deals with Visualizing Solid Shapes, students must ensure that they go through all the units thoroughly. Practicing these NCERT Solutions will help the students to answer the questions in their examination thoroughly. 

Given below are the NCERT Solutions for Exercise 10.1 Class 8 Maths that the students can download. 

Now that the students have their NCERT Solutions, they can kickstart their preparation accordingly. Given above are the images and the solutions that the students can refer to. However, students who want to access the complete NCERT Solutions for Exercise 10.1 Class 8 Maths can refer to the link given below:

NCERT Solutions Maths Class 8- All Chapter PDF Download

Given below are some of the PDF links for all chapters for NCERT Solutions for Class 8. The students can refer to the NCERT Solutions in order to download the PDF. These include:

Exercise 10.1 Class 8 Maths: About the Exercise

NCERT Solutions for Class 8 Exercise 10.1 follows a very basic approach. In unit 10.1, students have been introduced to the different types of solid figures. Therefore, in exercise 10.1, students must work on identifying each of these shapes. 

In this exercise, a solid shape is given along with two views. The students need to identify the two similar shapes and match them. This is a very basic exercise done to ensure that the students are familiar with each of the solid shapes and how to identify them. 

Exercise 10.1 Class 8 Maths NCERT Solutions is divided into different exercises. Each student needs to ensure that they follow the exercises carefully. In one of the exercises, the front and back views of the shapes are given. Students need to match and identify both ideas.

When dealing with solid shapes, students must identify what the top, front and side views are. Depending on that, the students can understand each view and implement them for their understanding. It is important that the students learn about different solid shapes in the initial stages. This will play an important role in helping the students understand and solve the complex problems related to shapes in the long run. 

Students in the later chapters of higher classes such as Class 9, 10 and more will need to practice the questions related to this chapter. Since it helps to build the foundation, of course, students can therefore excel in further classes in the long run. Make sure to follow all the questions given on Class 8 Maths Exercise 10.1 to help students prepare for their examination. 

NCERT Solutions for Class 8 Chapter 10: Chapter Summary

Solids have a proper shape and consume space. A strong is comprised of polygonal locales, which are called its countenances.

Polyhedron: A strong shape limited by polygons is called a polyhedron. Crystal: A crystal is strong, whose side countenances are parallelograms and whose closures (or bases) are consistent equal polygons. A crystal has 2 three-sided faces, 3 rectangular countenances, 6 vertices and 9 edges.

Pyramid: A pyramid is a polyhedron whose base is a polygon of quite a few sides and whose different countenances are triangles with a typical vertex. A pyramid has 1 square face, 4 three-sided faces, 5 vertices and 8 edges.

Tetrahedron: A pyramid is known as a three-sided pyramid on the off chance that its base is a triangle. A three-sided pyramid is likewise called a tetrahedron.

Plane shapes have two aspects (estimations) like length and broadness while a strong item has three estimations like length, expansiveness and level (or profundity). To that end they are called two-layered shapes and three-layered shapes, individually. They are momentarily named as 2-D and three-dimensional figures, separately. Triangles, square shapes, circles, and so forth, are 2-D figures while blocks, chambers, cones, circles, and so on, are three-dimensional figures.

Perspectives on three-dimensional Shapes: 3-layered objects look uniquely in contrast to various positions. Thus, they can be drawn according to alternate points of view like the top view, front view, and side view.

Benefits of referring to the Class 8 NCERT Solutions Exercise 10.1

Since Chapter 8 deals with visualising solid shapes, the students need to ensure that they prepare for the exams accordingly. Referring to the NCERT Solutions for Exercise 10.1 Class 8 can prove to be extremely helpful for the students. Some of the common benefits of referring to the NCERT Solutions for Exercise 10.1 include the following:

• The exercise 10.1 NCERT Solutions has been designed by academic experts at Embibe. Since it is written in a simple language, students can easily prepare for the exams accordingly. 
• Since the NCERT solutions are written in an easy to understand language, they can play an important role in helping the students solve their homework and assignments. 
• The NCERT Solutions cover all the fundamentals or basics of the chapter that can be extremely beneficial for the students to prepare for their examination. 
• The use of NCERT Solutions on a regular basis can be extremely beneficial for students who want to appear for competitive exams such as Olympiad. 
• Practicing from the NCERT Solutions can be of great help for strengthening the basics of the students. This can eventually pave the way for students to understand what the chapter is about and score higher marks in the examination. 

Students can refer to the Class 8 NCERT Solutions for understanding the different types of solid shapes and what type of formula can be applied while solving the questions on the same. 

Class 8 NCERT Solutions for Solid Shapes will further help students to revise the entire chapter in a very easy manner. Since students will be introduced to the concept of solid shapes for the first time. Thus, they will need the help of NCERT solutions for the preparation. 

Frequently Asked Questions on Exercise 10.1 NCERT Solutions

Students preparing for Class 8 may have certain questions related to NCERT Solutions, they must prepare for the examinations accordingly. Therefore, it is extremely crucial to follow all the questions related to the chapter. Given below are some of the frequently asked questions on Class 8 Maths Exercise 10.1 NCERT Solutions that can help to clarify the doubts of the students:

Q1: How many shapes are there in Chapter 10 Class 8? Ans: The NCERT Solutions for Chapter 10 Class 8 comprises the understanding of how any shape will occupy space. Some of the prominent two-dimensional figures covered in this chapter are rectangles, circles and triangles. Furthermore, the chapter also deals with the three-dimensional angles such as cubes, spheres, cylinders and cones. 

Q2: What are solid shapes in Maths?  Ans: The solid shapes are one of the most important chapters in Geometry. It defines the shape and figure that comprises two-dimensional and three-dimensional figures. These are often referred to as three-dimensional shapes. The study of the volume and properties of the surface area of two-dimensional and three-dimensional figures is known as Solid Shapes in Geometry. 

Q3: How many shapes are there in geometry?  Ans: There are different shapes of geometry depending on their dimension. Some of the most prominent two-dimensional shapes include triangle, circle, kite, square, rectangle, rhombus, parallelogram and trapezium. The chapter also comprises three-dimensional figures such as cone, cylinder, cube and cuboid. 

Q4: Where can students find the NCERT Solutions for Class 8 Chapter 10 Exercise 10.1? Ans: Students appearing for their Class 8 exams need to ensure that they follow all the NCERT Solutions. However, for Maths, Exercise 10.1 helps in understanding the concept of Solid Shapes. Students looking forward to preparing for Class 8 exams using NCERT Solutions. Students can download the NCERT Solutions from Embibe. Refer to the article given above to practice the exercises. 

 Q5. Are these Maths NCERT Solutions helpful for students?  Ans: Yes. Students in Class 8 must follow the NCERT Solutions for all subjects to excel in them. Students can check out the NCERT Solutions for Class 8 in Embibe and kickstart their preparation for the exams. 

The NCERT Solutions for Class 8 Maths Chapter 10 Exercise 10.1 deals with the view of 3D shapes. The 3D figure can look different in different positions. Similarly, they can be drawn from different perspectives depending on the approach of the learner. Having a pictorial representation of the same can make it easier for the students to identify each shape and thus implement it accordingly during their preparation. 

Students can download the NCERT Solutions for Class 8 from the table given below:

We hope this article on CBSE Class 8 Exercise 10.1 has been helpful for you. If you have any questions related to the chapter, drop them in the comments section below and we shall get back to you. 

Till then, stay tuned to Embibe to receive further updates on CBSE. 

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MCQ Questions for Class 8 Maths Chapter 10 Visualising Solid Shapes with Answers

October 1, 2020 by Veerendra

Check the below NCERT MCQ Questions for Class 8 Maths Chapter 10 Visualising Solid Shapes with Answers Pdf free download. MCQ Questions for Class 8 Maths with Answers were prepared based on the latest exam pattern. We have provided Visualising Solid Shapes Class 8 Maths MCQs Questions with Answers to help students understand the concept very well.

Students can also refer to NCERT Solutions for  Class 8 Maths Chapter 10 Visualising Solid Shapes for better exam preparation and score more marks.

Visualising Solid Shapes Class 8 MCQs Questions with Answers

Answer: (b) square

Answer: (c) cone

Answer: (d) cylinder

Answer: (a) triangle

Answer: (b) circle

Answer: (b) cube

Answer: (b) cuboid

Answer: (b) sphere

Question 9. A cuboid has how many faces ? (a) 2 (b) 4 (c) 6 (d) 3.

Answer: (c) 6

Question 10. How many faces does a cube have ? (a) 6 (b) 4 (c) 3 (d) 2.

Answer: (a) 6

Question 11. How many vertices does a cuboid have ? (a) 4 (b) 6 (c) 8 (d) 3.

Answer: (c) 8

Question 12. How many vertices does a cube have ? (a) 8 (b) 6 (c) 4 (d) 2.

Answer: (a) 8

Question 13. How many edges does a cuboid have ? (a) 12 (b) 8 (c) 6 (d) 4.

Answer: (a) 12

Question 14. How many edges does a cube have ? (a) 12 (b) 6 (c) 4 (d) 8.

Question 15. How many faces does a triangular pyramid have ? (a) 1 (b) 2 (c) 3 (d) 4.

Answer: (d) 4

Question 16. How many vertices does a triangular pyramid have ? (a) 1 (b) 2 (c) 3 (d) 4.

Question 17. How many edges does a triangular pyramid have ? (a) 2 (b) 4 (c) 6 (d) 8.

Question 18. How many faces does a triangular prism have ? (a) 5 (b) 4 (c) 3 (d) 6.

Answer: (a) 5

Question 19. How many vertices does a triangular prism have ? (a) 6 (b) 5 (c) 4 (d) 3.

Question 20. How many edges does a triangular prism have ? (a) 11 (b) 9 (c) 6 (d) 3.

Answer: (b) 9

Question 21. How many faces does a pyramid with square base have ? (a) 5 (b) 3 (c) 2 (d) 6.

Question 22. How many vertices does a pyramid with square base have ? (a) 5 (b)4 (c) 3 (d) 6.

Question 23. How many edges does a pyramid with square base have ? (a) 8 (b) 6 (c) 4 (d) 5.

Answer: (b) 7

Question 25. The number of vertices is (a) 5 (b) 7 (c) 8 (d) 10

Answer: (d) 10

Question 26. The number of edges is (a) 5 (b) 10 (c) 20 (d) 15.

Answer: (d) 15

Question 27. For a polyhedron, if ‘F’ stands for number of faces, V stands for number of vertices and E stands for number of edges, then which of the following relationships is named as Euler’s formula ? (a) F + V = E + 2 (b) F + E = V + 2 (c) V + E = F + 2 (d) F+ V = E – 2.

Answer: (a) F + V = E + 2

Question 28. A cube has ______ faces. (a) 4 (b) 5 (c) 6 (d) 8

Answer: (c) 6 Explanation: A cube is a three dimensional shape having six faces.

Question 29. A sphere has how many faces ? (a) One (b) Two (c) Four (d) None

Answer: (d) None Explanation: A sphere is a round-shaped object having no faces and edges.

Question 30. The top-view of a cone looks like: (a) A Circle (b) A Square (c) A Rectangle (d) A Triangle

Answer: (a) A Circle Explanation: The base of a right-cone is always circular. When we see it from the top, it looks like a circle with its vertex as the center of the circle.

Question 31. The top-view of a cube looks like a: (a) Circle (b) Square (c) Rectangle (d) Triangle

Answer: (b) Square Explanation: Since all the faces of a cube are of equal length.

Question 32. The base of a prism is: (a) Circle (b) Triangle (c) Square (d) Any shape

Answer: (d) Any shape Explanation: A pyramid is a polyhedron whose base is a polygon (of any number of sides) and whose lateral faces are triangles with a common vertex.

Question 33. If a polyhedron has 6 vertices and 12 edges. What is the number of faces it has ? (a) 6 (b) 8 (c) 12 (d) 18

Answer: (b) 8 Explanation: By Euler’s formula we know that: For any polyhedron, F + V – E = 2 F = 2 – V + E F = 2 – 6 + 12 = 8

Question 34. Number of vertices a cone has: (a) One (b) Two (c) Three (d) Four

Answer: (a) One

Question 35. An example of cone is: (a) Tube (b) A tent (c) A ball (d) A box

Answer: (b) A tent

Question 36. The top-view of a cuboid looks like a: (a) Circle (b) Square (c) Rectangle (d) Triangle

Answer: (c) Rectangle

Question 37. The side-view of a cone appears as: (a) Circle (b) Square (c) Rectangle (d) Triangle

Answer: (d) Triangle

We hope the given NCERT MCQ Questions for Class 8 Maths Chapter 10 Visualising Solid Shapes with Answers Pdf free download will help you. If you have any queries regarding Visualising Solid Shapes CBSE Class 8 Maths MCQs Multiple Choice Questions with Answers, drop a comment below and we will get back to you soon.

• Visualizing Solid Shapes Class 7 Case Study Questions Maths Chapter 13

Last Updated on September 7, 2024 by XAM CONTENT

Hello students, we are providing case study questions for class 7 maths. Case study questions are the new question format that is introduced in CBSE board. The resources for case study questions are very less. So, to help students we have created chapterwise case study questions for class 7 maths. In this article, you will find case study questions for CBSE Class 7 Maths Chapter 13 Visualizing Solid Shapes. It is a part of Case Study Questions for CBSE Class 7 Maths Series.

Table of Contents

Case Study Questions on Visualizing Solid Shapes

An ice-cream cart has an ice-candy drawn on all sides, except the top and the bottom

Q. 1. Which geometric shape does the ice-cream container resemble? (a) Cuboid (b) Cylinder (c) Cone (d) Pyramid

Ans. Option (a) is correct. Explanation: Cuboid

Q. 2. How many ice-candies are drawn on the cart? (a) 1 (b) 2 (c) 4 (d) 6

Ans. Option (c) is correct. Explanation: There are 4 ice-candies drawn on the cart.

• Symmetry Class 7 Case Study Questions Maths Chapter 12
• Exponents and Powers Class 7 Case Study Questions Maths Chapter 11
• Algebraic Expressions Class 7 Case Study Questions Maths Chapter 10
• Perimeter and Area Class 7 Case Study Questions Maths Chapter 9
• Rational Numbers Class 7 Case Study Questions Maths Chapter 8
• Comparing Quantities Class 7 Case Study Questions Maths Chapter 7
• Triangle and its Properties Class 7 Case Study Questions Maths Chapter 6
• Lines and Angles Class 7 Case Study Questions Maths Chapter 5
• Simple Equations Class 7 Case Study Questions Maths Chapter 4
• Data Handling Class 7 Case Study Questions Maths Chapter 3

Fractions and Decimals Class 7 Case Study Questions Maths Chapter 2

Integers class 7 case study questions maths chapter 1, topics from which case study questions may be asked.

• Plane figures and solid shapes
• Faces, edges and vertices of solid shapes
• Nets for building 3-D shapes
• Drawing solids on a flat surface
• Visualising different section of a solid

Plane figures are of two-dimensions and solid figures are of three-dimensions. In a solid figure, the corners are the vertices, the line segments are its edges and its flat surface are its faces.

A net is an arrangement of plane figures connected at their edges, lying in the same plane, that can be folded to make a three-dimensional solid.

Figures drawn on paper are called plane figure. Solid figures are those figures which occupy space.

Case study questions from the above given topic may be asked.

Plane figures are 2-dimensional, while solids are 3-dimensional. Visualising solid shapes is a very useful skill. You should be able to see ‘hidden’ parts of the solid shape.

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Frequently Asked Questions (FAQs) on Visualizing Solid Shapes Case Study

Q1: what are solid shapes.

A1: Solid shapes are three-dimensional figures that have length, breadth, and height. Common examples of solid shapes include cubes, cuboids, cones, and cylinders. Unlike two-dimensional shapes, these objects occupy space and can be viewed from different perspectives.

Q2: What is the difference between 2D and 3D shapes?

A2: 2D shapes have only two dimensions—length and breadth—and can be drawn on flat surfaces, like squares or circles. In contrast, 3D shapes have three dimensions—length, breadth, and height—like cubes or spheres. While 2D shapes can be represented easily on paper, 3D shapes are visualized as solid objects that occupy space.

Q3: What are oblique and isometric sketches?

A3: An oblique sketch is a simple way to represent a 3D object on a 2D plane. It gives a distorted view because one side is drawn at an angle. An isometric sketch , on the other hand, provides a more accurate representation of a solid object, with all dimensions to scale, giving a clearer idea of how the object looks from different angles

Q4: How can we visualize cross-sections of solids?

A4: Cross-sections are the shapes you get when you slice a solid object along a plane. For example, cutting a cylinder horizontally would give a circular cross-section, while cutting a cube horizontally or vertically would give a square cross-section.

Q5: How are shadows of 3D objects formed?

A5: Shadows of 3D objects depend on the shape of the object and the angle of light. For example, a cube can cast a square or rectangular shadow, while a cylinder can cast a circular or rectangular shadow based on how light falls on it. Visualizing shadows helps in understanding how 3D objects interact with light​.

Q6: What are polyhedrons?

A6: Polyhedrons are three-dimensional shapes with flat faces. Each face is a polygon, and the edges of the polygons meet at vertices. Common examples of polyhedrons include cubes (with square faces) and pyramids (with triangular faces). A polyhedron is named based on the shape and number of its faces.

Q7: How do you calculate the number of faces, edges, and vertices of a solid shape?

A7: For polyhedrons, the relationship between the number of faces (F), edges (E), and vertices (V) is given by Euler’s formula: V − E + F = 2 This formula helps in identifying the structure of a polyhedron. For example, a cube has 8 vertices, 12 edges, and 6 faces, satisfying Euler’s formula.

Q10: Are there any online resources or tools available for practicing Visualizing Solid Shapes case study questions?

A10: We provide case study questions for CBSE Class 7 Maths on our  website . Students can visit the website and practice sufficient case study questions and prepare for their exams. If you need more case study questions, then you can visit Physics Gurukul website. they are having a large collection of case study questions for all classes.

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