NCERT Solutions for Class 8 Maths Chapter 10 Visualising Solid Shapes Ex 10.3 are part of NCERT Solutions for Class 8 Maths. Here we have given NCERT Solutions for Class 8 Maths Chapter 10 Visualising Solid Shapes Ex 10.3.

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 8 |

Subject |
Maths |

Chapter |
Chapter 10 |

Chapter Name |
Visualising Solid Shapes |

Exercise |
Ex 10.3 |

Number of Questions Solved |
8 |

Category |
NCERT Solutions |

## 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.

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