These NCERT Solutions for Class 8 Maths Chapter 10 Visualizing Solid Shapes Ex 10.3 Questions and Answers are prepared by our highly skilled subject experts.

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

Question 1.

Can a polyhedron have for its faces.

(i) 3 triangles

(ii) 4 triangles

(iii) a square and four triangles?

Answer:

(i) No, it is not possible

(ii) Yes, four triangles can be the faces of a polyhedron.

(iii) Yes, a square and four triangles can be the faces.

Question 2.

Is it possible to have a polyhedron with any given number of faces?

(Hint: Think of a pyramid)

Answer:

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

Question 3.

Which are prisms among the following?

(i) A nail

(ii) Unsharpened pencil

Answer:

(i) No, a nail is not a prism.

(ii) Yes, unsharpened pencil is a prism.

(iii) No, table weight is not a prism.

(iv) Yes, box is a prism.

Question 4.

(i) How are prisms and cylinders alike?

(ii) How are pyramids and cones alike?

Answer:

(i) A prism becomes a cylinder as the number of sides of its base becomes larger and larger.

(ii) 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:

Answer:

No, it can be a cuboid also.

Question 6.

Verify Euler’s formula for these solids.

Answer:

In the given figure,

F = 7, V = 10 and E = 15

F + V – E = 7 + 10 – 15 = 17 – 15

F + V – E = 2

Thus, Euler’s formula is verified.

(ii) In the given figure,

F = 9, V = 9 and E = 16

F + V- E = 9 + 9 – 16 = 18 – 16

Thus, Euler’s formula is verified.

Question 7.

Using Euler’s formula find the unknown.

Answer:

(i) Here V = 6 and E = 12

F + V – E = 2

F + 6 – 12 = 2

F – 6 = 2

F = 6 + 2 = 8

(ii) F = 5, E = 9

F + V – E = 2

5 + V – 9 = 2

V – 4 = 2

V = 2 + 4 = 6

(iii) Here F = 20 V = 12

F + V – E = 2

20 + 12 – E = 2

32 – E = 2

32 – 2 = E

30 = E

Question 8.

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

Answer:

Here, F = 10, E = 20, V = 15

We know that F + V – E = 2

Here, F + V – E =10 + 15 – 20

= 25 – 20

= 15 ≠ 2

∴ Such a polyhedron is not possible.