Punjab State Board PSEB 8th Class Maths Book Solutions Chapter 10 Visualising Solid Shapes Ex 10.3 Textbook Exercise Questions and Answers.

## PSEB Solutions for Class 8 Maths Chapter 10 Visualising Solid Shapes Ex 10.3

1. Can a polyhedron have for its faces:

Question (i)

3 triangles?

Solution:

[Note: Polyhedron is a solid, which is made by polygonal regions and these polygonal regions are called its faces.]

No, a polyhedron cannot have 3 triangles for its faces because it have atleast 4 faces.

Question (ii)

4 triangles?

Solution:

Yes, a polyhedron can have 4 triangles for its faces as triangular pyramid.

Question (iii)

a square and four triangles?

Solution:

Yes, a polyhedron can have a square and four triangles for its faces as a pyramid with square base.

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

Solution:

Yes, it can be possible only if the number of faces is greater than or equal to 4, because a polyhedron has atleast 4 faces.

3. Which are prisms among the following?

Solution:

Note: A prism is a polyhedron whose base and top are congruent polygons and lateral faces are rectangles.

(i) No, a nail is not a prism because its base and top are not congruent polygons.

(ii) Yes, an unsharpened pencil is a prism because its base and top are congruent polygons and faces are rectangles.

(iii) No, a table weight is not a prism because its top and base are not congruent polygons.

(iv) Yes, box is a prism because its base and top are congruent polygons and lateral faces are rectangles.

4.

Question (i)

How are prisms and cylinders alike?

Solution:

Top and base of a prism and of a cylinder are congruent and parallel to each other and a prism becomes a cylinder, if the number of sides of its base becomes larger and larger.

Question (ii)

How are pyramids and cones alike?

Solution:

The pyramids and cones are alike because their lateral faces meet at a vertex. Also, a pyramid becomes a cone if the number of sides of its base becomes larger and larger.

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

Solution:

No, a square prism is not same as a cube. It can be a cuboid also.

6. Verify Euler’s formula for these solids:

Solution:

(i) For figure (i)

F = 7, V= 10 and E = 15

∴ F + V = 7 + 10 = 17

Now, F + V – E = 17 – 15 = 2

Thus, F + V – E = 2

Hence, Euler’s formula is verified.

(ii) For figure (ii)

F = 9, V = 9 and E = 16

∴ F + V = 9 + 9 = 18

Now, F + V – E = 18 – 16 = 2

Thus, F + V – E = 2

Hence, Euler’s formula is verified.

7. Using Euler’s formula find the unknown:

(i) | (ii) | (iii) | |

Faces | ? | 5 | 20 |

Vertices | 6 | ? | 12 |

Edges | 12 | 9 | ? |

Solution:

(i) Here, F = ?, V = 6 and E = 12

Now, F + V – E = 2 (∵ Euler’s formula)

∴ F + 6 – 12 = 2

∴ F – 6 = 2

∴ F = 2 + 6

∴ F = 8

(ii) Here, F = 5, V = ? and E = 9

Now, F + V – E = 2 (∵ Euler’s formula)

∴ 5 + V – 9 = 2

∴ V – 4 = 2

∴ V = 2 + 4

∴ V = 6

(iii) Here, F = 20, V = 12 and E = ?

Now, F + V – E = 2 (∵ Euler’s formula)

∴ 20 + 12 – E = 2

∴ 32 – E = 2

∴ – E = 2 – 32

∴ – E = – 30

∴ E = 30

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

Solution:

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

By Euler’s formula, F + V – E = 2

LHS = F + V – E

= 10 + 15 – 20

= 25 – 20 = 5

Thus, F + V – E ≠ 2

Hence, such a polyhedron is not possible.