Chapter 10 Visualising Solid Shapes

**NCERT Solutions for Class 8 Maths Chapter 10 Visualising Solid Shapes Ex 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.

**Solution.**

**Question 2.**

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

**Solution.**

**Question 3.**

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

**Solution.**

**Question 4.**

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

**Solution.**

**NCERT Solutions for Class 8 Maths Chapter 10 Visualising Solid Shapes Ex 10.2**

**Question 1.**

Look at the given map of a city.

**Answer the following.**

**(a)** Colour the map as follows: Bluewater, Red-fire station, Orange-Library, Yellow-schools, Green-Parks, Pink-Community Centre, 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?

**Solution.**

**(a)** Please color yourself.

**(b)** See the above figure.

**(c)** See the above figure.

**(d)** City Park.

**(e)** Senior Secondary school.

**Question 2.**

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

**Solution.**

Please draw yourself.

**Question 3.**

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

**Solution.**

Please draw yourself.

**Question 4.**

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

**Solution.**

Please draw yourself.

**NCERT Solutions for Class 8 Maths Chapter 10 Visualising Solid Shapes Ex 10.3**

**Question 1.**

**Can a polyhedron have for its faces**

**(i)** 3 triangles?

**(ii)** 4 triangles?

**(iii)** a square and four triangles?

**Solution.**

**(i)** No

**(ii)** Yes

**(iii)** Yes

**Question 2.**

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

**Solution.**

Possible, only if the number of faces is greater than or equal to 4.

**Question 3.**

Which are prisms among the following?

**Solution.**

We know that a prism is a polyhedron whose base and top faces are congruent and parallel and other (lateral) faces are parallelograms in shape. So, only (ii) and (iv) are prisms.

**Question 4.**

**(i)** How are prisms and cylinders alike?

**(ii)** How are pyramids and cones alike?

**Solution.**

**(i)** The prisms and cylinder, both, have their base and top faces as congruent and parallel to each other. Also, a prism becomes a cylinder as the number of sides of its base becomes larger and larger.

**(ii)** The pyramids and cones are alike in the sense that their lateral faces meet at a point (called vertex). Also, a pyramid becomes a cone as the number of sides of its base becomes larger and larger.

**Question 5.**

Is a square prism same as a cube ? Explain.

**Solution.**

No; not always as it can be a cuboid also.

**Question 6.**

Verify Euler’s formula for these solids

**Solution.**

**(i)**

F = 7

V= 10

E = 15

F + V = 7 + 10 = 17

E + 2 = 15 + 2 = 17

So, F + V = E + 2

Hence, Euler’s Formula is verified,

**(ii)**

F = 9

V = 9

E = 16

F + V = 9 + 9 = 18

E + 2 = 16 + 2 = 18

So, F + V = E + 2

Hence, Euler’s Formula is verified

**Question 7.**

Using Euler’s formula find the unknown.

**Solution.**

**(i)**

F + V = E + 2

⇒ F + 6 = 12 + 2

⇒ F + 6 = 14

⇒ F = 14 – 6 = 8

**(ii)**

F + V = E + 2

⇒ 5 + V = 9 + 2

⇒ 5 + V = 11

⇒ V= 11-5 = 6

**(iii)**

F + V = E + 2

⇒ 20 + 12 = E + 2

⇒ 32 = E + 2

⇒ E = 32 – 2

⇒ E = 30

**Question 8.**

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

**Solution.**

Here F = 10

E = 20

V= 15

So, F + V = 10 + 15 = 25

E + 2 = 20 + 2 = 22

∵ F + V ≠ E + 2

∴ Such a polyhedron is not possible.