## 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 â€“ Visualising Solid Shapes solved by Expert Maths Teachers on CoolGyan.Org. All Chapter 10 â€“ 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)**Â No, a polyhedron cannot have 3 triangles for its faces.

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

**(iii)**Â 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.Â **It is possible, only if the number of faces are greater than or equal to 4.

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

**Ans.Â**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)Â**A prism becomes a cylinder as the number of sides of its base becomes larger and larger.

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

**6. Verify Eulerâ€™s formula for these solids.**

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

Using Euclerâ€™s formula, we see

F + V â€“ E = 2

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

F + V â€“ E = 2

Â 7 + 10 â€“ 15 = 2

Â 17 â€“ 15 = 2

Â 2 = 2

Â L.H.S. = R.H.S.Â Hence Euclerâ€™s formula verified.

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

Using Euclerâ€™s formula, we see

F + V â€“ E = 2

F + V â€“ E = 2

Â 9 + 9 â€“ 16 = 2

Â 18 â€“ 16 = 2

Â 2 = 2

Â L.H.S. = R.H.S.

Hence Euclerâ€™s formula verified.

**7. Using Eulerâ€™s formula, find the unknown:**

Faces |
? |
5 |
20 |

Vertices |
6 |
? |
12 |

Edges |
12 |
9 |
? |

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

Using Euclerâ€™s formula, we see

F + V â€“ E = 2

F + V â€“ E = 2

Â F + 6 â€“ 12 = 2

Â F â€“ 6 = 2

Â F = 2 + 6 = 8

Hence there are 8 faces.

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

Using Euclerâ€™s formula, we see

F + V â€“ E = 2

F + V â€“ E = 2

Â 5 + V â€“ 9 = 2

Â V â€“ 4 = 2

Â V = 2 + 4 = 6

Hence there are 6 vertices.

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

Using Euclerâ€™s formula, we see

F + V â€“ E = 2

F + V â€“ E = 2

Â 20 + 12 â€“ E = 2

Â 32 â€“ E = 2

Â E = 32 â€“ 2 = 30

Hence there are 30 edges.

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

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

Then, we know Using Euclerâ€™s formula,

F + V â€“ E = 2

L.H.S. = F + V â€“ E

= 10 + 15 â€“ 20

= 25 â€“ 20

= 5

R.H.S.Â = 2

Â L.H.S.Â â‰ â‰ Â R.H.S.

Therefore, it does not follow Euclerâ€™s formula.

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