## ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 17 Visualising Solid Shapes Ex 17.2

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.

Which are prisms among the following?

Solution:

Prisms are only (i) and (iv).

Question 3.

Verify Euler’s formula for these solids:

Solution:

Question 4.

Can a polyhedron have 15 faces, 30 edges and 20 vertices?

Solution:

Can a polyhedron have 15 faces, 30 edges and 20 vertices.

∵ F + V = E + 2

⇒ 15 + 20 = 35 and 30 + 2 = 32

∵ 35 ≠ 32

∴ It has not.

Question 5.

If a polyhedron has 8 faces and 8 vertices, find the number of edges.

Solution:

A polyhedron has 8 faces and 8 vertices.

∴ Number of edges = F + V – 2 = 8 + 8 – 2 = 14

Question 6.

If a polyhedron has 7 faces and 10 vertices, find the number of edges.

Solution:

A polyhedron has 7 faces and 10 vertices.

∴ Number of edges = F + V – 2 = 7 + 10 – 2 = 15

Question 7.

Write the number of faces, vertices and edges in

(i) an octagonal prism

(ii) decagonal pyramid.

Solution:

Question 8.

Using Euler’s formula, complete the following table:

Solution: