Mathematics NCERT Grade 8, Chapter 10: Visualising Solid Objects - The chapter lays emphasis on different solid shapes. Ever wondered difference between 2D and 3D shapes. Students will get all answers about the same. Recognizing 2D and 3D objects and different shapes are explained in detail to clear all the doubts of the students about the same. Features of 3D objects will be made clear to students.
• 3D objects have different views from different positions.
• Front, side and top view are the different views that one will study in this chapter through cubical blocks and 3-dimensional shapes.
Section 10.3 puts focus on the topic- Mapping Space Around Us. This section is supplemented with examples as well as short questions.
• A map depicts the location of a particular object/place in relation to other objects/places.
• Symbols are used to depict the different objects/places.
The last section of the chapter- Visualising Solid Objects, concept of faces, edges and vertices will be discussed. Concept of polyhedrons are introduced to students in this chapter. Definitions explained in the section are as follows:
• Faces
• Edges
• Vertex
• Polyhedron
• Non-polyhedron
• Convex polyhedron
• Regular polyhedrons
• Prism
• Pyramids
Euler's formula is an important formula relating the face, vertex and edge of a polyhedron.
F + V = E + 2
where F stands for number of faces, V stands for number of vertices and E stands for number of edges.
Three unsolved exercises are given for the assessment of students. The last exercise is 10.3 consisting of 8 questions. Questions are given in different patterns which makes the exercise more attractive and interesting for students.
9 points are listed in the summary of chapter in the end.

#### 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     #### Question 2:

For each of the given solid, the three views are given. Identify for each solid the corresponding top, front and side views. (a) (i) Front (ii) Side (iii) Top

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

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

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

#### Question 3:

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

(a) (b) (c) (d) (e) (a) (i) Top (ii) Front/Side (iii) Side/Front

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

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

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

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

#### Question 4:

Draw the front view, side view and top view of the given objects.  (a) A military tent (b) A table  (c) A nut (d) A hexagonal block  (e) A dice (f) A solid

(a)

 A military tent Front View Top View Side View (b)

 A table Front View Top View Side View (c)

 A nut Front View Top View Side View (d)

 A hexagonal block Front View Top View Side View (e)

 A dice Front View Top View Side View (f)

 A solid Front View Top View Side View #### Question 1:

Look at the given map of a city. (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.
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##### Video Solution for visualising solid shapes (Page: 163 , Q.No.: 1)

NCERT Solution for Class 8 maths - visualising solid shapes 163 , Question 1

#### Question 1:

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. #### Question 2:

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.

#### Question 3:

Which are prisms among the following?  (i) (ii)  (iii) (iv)

(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.

#### Question 4:

(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 maths - visualising solid shapes 166 , Question 5

#### Question 6:

Verify Euler’s formula for these solids.  (i) (ii)

(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 maths - visualising solid shapes 166 , Question 6

#### Question 7:

Using Euler’s formula, find the unknown.

 Faces ? 5 20 Vertices 6 ? 12 Edges 12 9 ?

By Euler’s formula, we have

F + V − E = 2

(i) F + 6 − 12 = 2

F − 6 = 2

F = 8

(ii) 5 + V − 9 = 2

V − 4 = 2

V = 6

(iii) 20 + 12 − E = 2

32 − E = 2

E = 30

Thus, the table can be completed as

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

##### Video Solution for visualising solid shapes (Page: 167 , Q.No.: 7)

NCERT Solution for Class 8 maths - 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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