## NCERT Solutions for Class 8 Chapter 10 Visualising Solid Shapes -Free PDF Download

Free PDF download of NCERT Solutions Maths Class 8 Solutions Chapter 10 – Visualising Solid Shapes solved by Expert Maths Teachers on CoolGyan.Org. All Chapter 10 – Visualising Solid Shapes Questions with Solutions for NCERT to help you to revise complete Syllabus and Score More marks.

Maths Revision Notes for Class 8

Chapter Name | Visualising Solid Shapes |

Chapter | Chapter 10 |

Exercise | Exercise 10.2 |

Class | Class 8 |

Subject | Maths NCERT Solutions |

Board | CBSE |

TEXTBOOK | CBSE NCERT |

Category | NCERT Solutions |

**NCERT SOLVED**

**1. Can a polygon have for its faces:**

**(i) 3 triangles (ii) 4 triangles (iii) a square and four triangles**

**Ans. (i)** No, a polyhedron cannot have 3 triangles for its faces.

**(ii)** Yes, a polyhedron can have four triangles which is known as pyramid on triangular base.

**(iii)** Yes, a polyhedron has its faces a square and four triangles which makes a pyramid on square base.

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

**Ans. **It is possible, only if the number of faces are greater than or equal to 4.

**3. Which are prisms among the following: **

**Ans. **Figure (ii) unsharpened pencil and figure (iv) a box are prisms.

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

**Ans. (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.

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

**Ans. **Yes, a square prism is same as a cube, it can also be called a cuboid. A *cube* and a *square prism* are both special types of a rectangular *prism*. A *square* is just a special type of rectangle! *Cubes* are rectangular prisms where all three dimensions (length, width and height) have the *same* measurement.** **

**6. Verify Euler’s formula for these solids.**

**Ans. (i) **Here, figure (i) contains 7 faces, 10 vertices and 15 edges.

Using Eucler’s formula, we see

F + V – E = 2

Putting F = 7, V = 10 and E = 15,

F + V – E = 2

7 + 10 – 15 = 2

17 – 15 = 2

2 = 2

L.H.S. = R.H.S. Hence Eucler’s formula verified.

**(ii)** Here, figure (ii) contains 9 faces, 9 vertices and 16 edges.

Using Eucler’s formula, we see

F + V – E = 2

F + V – E = 2

9 + 9 – 16 = 2

18 – 16 = 2

2 = 2

L.H.S. = R.H.S.

Hence Eucler’s formula verified.

**7. Using Euler’s formula, find the unknown:**

Faces | ? | 5 | 20 |

Vertices | 6 | ? | 12 |

Edges | 12 | 9 | ? |

**Ans. **In first column, F = ?, V = 6 and E = 12

Using Eucler’s formula, we see

F + V – E = 2

F + V – E = 2

F + 6 – 12 = 2

F – 6 = 2

F = 2 + 6 = 8

Hence there are 8 faces.

In second column, F = 5, V = ? and E = 9

Using Eucler’s formula, we see

F + V – E = 2

F + V – E = 2

5 + V – 9 = 2

V – 4 = 2

V = 2 + 4 = 6

Hence there are 6 vertices.

In third column, F = 20, V = 12 and E = ?

Using Eucler’s formula, we see

F + V – E = 2

F + V – E = 2

20 + 12 – E = 2

32 – E = 2

E = 32 – 2 = 30

Hence there are 30 edges.

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

**Ans.** If F = 10, V = 15 and E = 20.

Then, we know Using Eucler’s formula,

F + V – E = 2

L.H.S. = F + V – E

= 10 + 15 – 20

= 25 – 20

= 5

R.H.S. = 2

L.H.S. ≠≠ R.H.S.

Therefore, it does not follow Eucler’s formula.

So polyhedron cannot have 10 faces, 20 edges and 15 vertices.