NCERT Solutions for Class 8 Maths Chapter 10 Visualising Solid Shapes

1.Look at the given map of a city.


Answer the following.

(a) Colour the map as follows: Blue-water, 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?

Answer :

(a)The colored map is shown as:


(b)Marking is done as:



(c)The shortest route is shown in the red color as:



(d)The city Park is further east

(e)Sr. Secondary School is further south.

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

Answer :

You can describe your classroom as your wish.A sample is shown here as:

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

Answer :

Observe the different places things and areas to describe your school with the help of a suitable diagram.

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

Answer :

Describe the streets of your house showing proper turnings and pathways and give instructions step wise telling her to move along the various named streets.

1.Can a polyhedron have for its faces
(i) 3 triangles?

(ii) 4 triangles?

(iii) a square and four triangles?

Answer :

A polyhedron is a solid which is bounded by four or more polygonal faces in such a way that pairs of faces meet along edges and three or more edges meet in each vertex.Therefore,
(i)No because a polyhedron cannot for its faces have three triangles.

(ii)Yes



(iii)Yes

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

Answer :

Yes, it is possible only if the number of faces are equal or greater than four.

3.Which are prisms among the following ?

Answer :

Here we have only (ii) unsharpened pencils and (iv) a box as the prism.

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

Answer :

(i) If the number of sides of its base becomes larger and larger then a prism becomes a cylinder.
(ii) If the number of sides of its base becomes larger and larger then a pyramid becomes a cone

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

Answer :

Yes it can be but every square prism cannot be cube. It may be cuboid also.

6.Verify Euler’s formula for these solids.

Answer :

(i) In this given figure we have,
F = 7, V = 10, E =15

∴ F + V =7 + 10 = 17 and E + 2 =15 + 2 = 17

\(\Rightarrow\) F+V=E+ 2

Thus, Euler’s formula is verified.

(ii) In this given figure,

F =9, V = 9,E =16

∴ F + V =9 + 9 =18 and E + 2 =16 +2 =18

\(\Rightarrow\) F + V =E + 2

Thus, Euler’s formula is verified.

7.Using Euler’s formula find the unknown.

Answer :

In the first case we have: Vertices =6, Edges =12
By Euler’s formula, F + V= E + 2

F= 12 + 2-6 =8

Hence, faces =8

In 2nd case we have : Faces = 5, Edges = 9

By Euler’s formula, F + V = E + 2

V = E + 2 – F = 9+ 2- 5 = 6

Hence, vertices =6

In 3rd case we have : Faces =20, Vertices =12

By Euler’s formula, we know that F+V=E+2

E = F + V – 2 = 20 + 12 – 2 = 30

Hence, edges =30

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

Answer :

Since F + V \(\neq\) E +2 (as 10 +15 ? 20 + 2) so a polyhedron cannot have 10 faces, 20 edges and 15 vertices.