# NCERT Solutions for Class 8 Maths Chapter 10 Visualizing Solid Shapes

NCERT Solutions for Class 8 Maths Chapter 10 Visualizing Solid Shapes- You have already learnt about the 2D geometry in which basic shapes like a circle, a rectangle, square or rhombus are measured by length and width. We live in a 3-Dimensional world where every object that we can see or touch has three dimensions length, width, and height. For example, the room can be described by 3-dimensions length, width, and height. In this article, you will get NCERT solutions for Class 8 Maths chapter 10 Visualizing Solid Shapes that are prepared and explained in a detailed manner to clear your doubts. In this chapter, you will study solid objects like cubes, cuboids, cones, spheres, hemispheres, etc. You must have noticed that 3-dimensional objects look different when you look from different positions or different angles. To simplify its study there are defined viewpoints (front view, side view, top view) for the 3D object.

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In NCERT solutions for Class 8 Maths chapter 10 Visualizing Solid Shapes, maximum questions are related to finding front view, side view, and top view of the 3D geometry. Important topics like views of 3D shapes, mapping space around us, faces, edges, and vertices of the objects are covered in this chapter. NCERT solutions for Class 8 Maths chapter 10 Visualizing Solid Shapes are very helpful in engineering drawing, locating the place and will build a basic understanding of the 3D shapes. You can find NCERT Solutions from Classes 6 to 12 by clicking on the above link. Here you will get the detailed NCERT Solutions for Class 8 by clicking on the link.

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## NCERT Solutions for Class 8 Maths Chapter 10 Visualizing Solid Shapes Topic 10.1 Introduction

Question:1 Match the following: (First one is done for you)

Matched items are:

Question:2 Match the following pictures (objects) with their shapes:

Picture (object)

Shape

(i) An agricultural field

Two rectangular cross paths inside a rectangular park.

(ii) A groove

A circular path around a circular ground.

(iii) A toy

A triangular field adjoining a square field.

(iv) A circular park

A cone has been taken out of a cylinder.

(v) A cross path

A hemisphere surmounted on a cone.

Matched objects are:

## NCERT Solutions for Class 8 Chapter 10 Visualizing Solid Shapes-Exercise: 10.1

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

Object Side view Top view

Matched objects are:

(1) →iii)→iv)

(2) →i) →v)

(3) →iv)→ii)

(4) →v) →iii)

(5) →ii) →i)

Question:2(a) For each of the given solid, the three views are given. Identify for each solid the corresponding top,
front and side views.

(a) Different views have given: (i) Front, (ii) Side, (iii) Top.

Question:2(b) For each of the given solid, the three views are given. Identify for each solid the corresponding top,
front and side views.

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

Question:2(c) For each of the given solid, the three views are given. Identify for each solid the corresponding top,
front and side views.

(c) (i) Front view, (ii) Side view, and (iii) Top view.

Question:2(d) For each of the given solid, the three views are given. Identify for each solid the corresponding top,
front and side views.

(d) (i) Front view, (ii) Side view, and (iii) Top view.

Question:3(a) For each given solid, identify the top view, front view and side view.

(a) (i) Top view, (ii) Front/ Side view, and (iii) Side/ Front view.

Question:3(b) For each given solid, identify the top view, front view and side view.

(b) (i) Side view, (ii) Front view, and (iii) Top view.

Question:3(c) For each given solid, identify the top view, front view and side view.

(c) (i) Top view, (ii) Side view, and (iii) Front view.

Question:3(d) For each given solid, identify the top view, front view and side view.

(d) (i) Side view, (ii) Front view, and (iii) Top view.

Question:3(e) For each given solid, identify the top view, front view and side view.

(e) (i) Front view, (ii) Top view, and (iii) Side view.

Question:4(a) Draw the front view, side view and top view of the given objects.

A military tent

The front view, top view, and side view of a tent are shown below:

The front view, top view, and side view of a tent are shown below:

Question:4(b) Draw the front view, side view and top view of the given objects.

A table

The front view, top view, and Side view of the table are shown below:

Question:4(c) Draw the front view, side view and top view of the given objects.

A nut

The front, top, and side views of the nut are:

Question:4(d) Draw the front view, side view and top view of the given objects.

A hexagonal block

The front view, side view and top view of the hexagonal block are shown below:

Question:4(e) Draw the front view, side view and top view of the given objects.

The front view, side view and top view of the dice as shown below:

Question:4(f) Draw the front view, side view and top view of the given objects.

A solid

The front view, side view and top view of the given solid.

## NCERT Solutions for Class 8 Maths Chapter 10 Visualizing Solid Shapes-Exercise: 10.2

Question:1(a) Look at the given map of a city.

Colour the map as follows: Blue-water, red-fire station, orange-library, yellow
schools, Green - park, Pink - College, Purple - Hospital, Brown - Cemetery.

(a) Coloured map shown:

Question:1(b) Look at the given map of a city.

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) marked points of intersections "X" and "Y":

Question:1(c) Look at the given map of a city.

In red, draw a short street route from Library to the bus depot.

Route from Library to bus depot is shown:

Question:1(d) Look at the given map of a city.

Which is further east, the city park or the market?

(d) The city park is further east.

Question:1(e) Look at the given map of a city.

Which is further south, the primary school or the Sr. Secondary School?

(e) Sr. Secondary School is further south.

Question:2 Draw a map of your class room using proper scale and symbols for different objects.

Do it yourself.

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

Do it with your own imagination.

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

Do it with your own imagination.

## NCERT Solutions for Class 8 Maths Chapter 10 Visualizing Solid Shapes Topic 10.4 Faces, Edges and Vertices

Question:1 Tabulate the number of faces, edges and vertices for the following polyhedrons: (Here ‘V’ stands for number of vertices, ‘F’ stands for number of faces and ‘E’ stands for number of edges).What do you infer from the last two columns? In each case, do you find, i.e., ? This relationship is called Euler’s formula. In fact this formula is true for any polyhedron.

Solid

F

V

E

F+V

E+2

Cuboid

Triangular pyramid

Triangular prism

Pyramid with square base

Prism with square base

 Solid F V E F+V E+2 Cuboid 6 8 12 14 14 Triangular pyramid 4 4 6 8 8 Triangular prism 5 6 9 11 11 Pyramid with square base 5 5 8 10 10 Prism with square base 6 8 12 14 14

## NCERT Solutions for Class 8 Maths Chapter 10 Visualizing Solid Shapes-Exercise: 10.3

Question:1(i) Can a polyhedron have for its faces

3 triangles?

(i) No, a polyhedron cannot have 3 triangles for its faces .

Question:1(ii) Can a polyhedron have for its faces

4 triangles?

(ii) Yes, a polyhedron having 4 triangles is pyramid on triangular base.

Question:1(iii) Can a polyhedron have for its faces

a square and four triangles?

(iii) Yes, a polyhedron can have faces of a square and four triangles which makes a pyramid on square base.

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

Yes , it is possible if the number of faces is four or more than four.

Question:3(i) Which are prisms among the following?

(i) a nail is not a prism.

Question:3(ii) Which are prisms among the following?

(ii) The unsharpened pencil is a prism.

Question:3(iii) Which are prisms among the following?

(iii) Table weight is not a prism.

Question:3(iv) Which are prisms among the following?

(iv) Given box is a prism.

Question:4(i) How are prisms and cylinders alike?

(i) A prism is a polyhedron whose base and top are congruent polygons and whose other faces, i.e., lateral faces are parallelograms in shape. Also, the cylinder has base on top and bottom and faces are parallel.

Question:5 Is a square prism same as a cube? Explain.

No , not always, because it can be a cuboid also when extended.

Question:6(i) Verify Euler’s formula for these solids.

(i) Euler formula F+V = E + 2.

So, Number of faces (F) = 7, Number of vertices (V) = 10 and number of edges (E) = 15.

Hence putting in the formula; we get,

7 + 10 = 15 + 2

17 = 17 hence, it satisfies the Euler formula.

Question:6(ii) Verify Euler’s formula for these solids. Answer:

(ii) Euler formula F+V = E + 2.

So, Number of faces (F) = 9, Number of vertices (V) = 9 and number of edges (E) = 16.

Hence putting in the formula; we get,

9 + 9 = 16 + 2

18 = 18 hence, it satisfies the Euler formula.

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

We know the Euler Formula:

F + V = E + 2 :

hence we can easily find the unknown let say 'F, V, and E'

So, For Ist case:

F + 6 = 12 + 2 or F = 8, hence the number of faces in Ist case is 8.

For IInd Case;

5 + V = 9 + 2 or V = 6, hence the number of vertices in IInd case is 6.

For IIIrd case;

20 + 12 = E + 2 or E = 30, hence the number of Edges in the IIIrd case is 30.

 Faces 8 5 20 Vertices 6 6 12 Edges 12 9 30

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

Checking using Euler's Formula:

F + V = E +2;

Given that F = 10, V = 15 and E = 20 so,

Putting in equation: 10 + 15 = 35 and 20 +2 = 22

Hence, given polyhedron having 10 faces, 20 edges and 15 vertices is not possible.

## Visualizing Solid Shapes Class 8 Math Chapter 10-Topics

• Views of 3D-Shapes
• Mapping Space Around Us
• Faces, Edges, and Vertices

### NCERT Solutions for Class 8 Maths: Chapter-Wise

 Chapter -1 Rational Numbers Chapter -2 Linear Equations in One Variable Chapter-3 Understanding Quadrilaterals Chapter-4 Practical Geometry Chapter-5 Data Handling Chapter-6 Squares and Square Roots Chapter-7 Cubes and Cube Roots Chapter-8 Comparing Quantities Chapter-9 Algebraic Expressions and Identities Chapter-10 Visualizing Solid Shapes Chapter-11 Mensuration Chapter-12 Exponents and Powers Chapter-13 Direct and Inverse Proportions Chapter-14 Factorization Chapter-15 Introduction to Graphs Chapter-16 Playing with Numbers

### NCERT Solutions for Class 8: Subject-Wise

• NCERT Solutions for Class 8 Maths
• NCERT Solutions for Class 8 Science

In NCERT solutions for class 8 maths chapter 10 visualizing solid shapes only one formula has been used know as Euler’s formula.

For any polyhedron-

where F - Number of faces

V - Number of vertices

E - Number of edges

As the name suggests this chapter is more about visualizing the shapes and drawing the front view, side view, and top view. In exercise 1 and 2 of NCERT solutions for class 8 maths chapter 10 visualizing solid shapes, most questions are related to visualizing shape and mapping which are explained with the help of drawing and graphs.

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