NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes Ex 13.6 are part of NCERT Solutions for Class 9 Maths. Here we have given NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes Ex 13.6.

- Surface Areas and Volumes Class 9 Ex 13.1
- Surface Areas and Volumes Class 9 Ex 13.2
- Surface Areas and Volumes Class 9 Ex 13.3
- Surface Areas and Volumes Class 9 Ex 13.4
- Surface Areas and Volumes Class 9 Ex 13.5
- Surface Areas and Volumes Class 9 Ex 13.6
- Surface Areas and Volumes Class 9 Ex 13.7
- Surface Areas and Volumes Class 9 Ex 13.8
- Surface Areas and Volumes Class 9 Ex 13.9

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 9 |

Subject |
Maths |

Chapter |
Chapter 13 |

Chapter Name |
Surface Areas and Volumes |

Exercise |
Ex 13.6 |

Number of Questions Solved |
8 |

Category |
NCERT Solutions |

## NCERT Solutions for Class 9 Maths Chapter 13 Surface Areas and Volumes Ex 13.6

**Assume π = unless stated otherwise.**

Question 1.

The circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm. How many liters of water can it hold? (1000 cm^{3} = 1 L)

Solution.

Let r be the radius of cylindrical vessel.

We have, circumference of the base = 132 cm

∴ 2πr = 132

Question 2.

The inner diameter of a cylindrical wooden pipe is 24 cm and its outer diameter is 28 cm. The length of the pipe is 35 cm. Find the mass of the pipe, if 1 cm^{3} of wood has a mass

Solution.

Question 3.

**A soft drink is available in two packs :
**(i) a tin can with a rectangular base of length 5 cm and width 4 cm, having a height of 15 cm and

(ii) a plastic cylinder with circular base of diameter 7 cm and height 10 cm. Which container has greater capacity and by how much?

Solution.

**(i)**We have, h = 15 cm l = 5 cm, b = 4 cm

Volume of cuboidical body =l x b x h = 5 x 4 x 15 = 300 cm

^{3}…(i)

Question 4.

If the lateral surface area of a cylinder is 94.2 cm^{2} and its height is 5 cm, then find

(i) radius of its base,

(ii) its volume, (use, π = 3.14)

Solution.

**(i)** Let r be the radius of the base.

We have, height (h) = 5 cm and lateral surface area of a cylinder = 94.2 cm^{2
}∴ 2πrh = 94.2

2 x 3.14 x r x 5 = 94.2

⇒ r =

⇒ r = 3 cm

Hence, radius of base (r) = 3 cm

**
(ii)** Volume of a cylinder = πr

^{2}h = 3.14 x (3)

^{2}x 5

= 3.14 x 9 x 5 = 141.3cm

^{3}

Question 5.

It costs Rs. 2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of? 20 per m^{2}, find

(i) inner curved surface area of the vessel,

(ii) radius,of the base,

(iii) capacity of the vessel.

Solution.

(i) Inner curved surface area of the vessel = 110 m^{2
}(ii) Hence, radius of the base is 1.75 m.

Question 6.

The capacity of a closed cylindrical vessel of height 1 m is 15.4 L. How many square metres of metal sheet would be needed to make it?

Solution.

Let r be the radius of the vessel.

Given, capacity of a closed cylindrical vessel = 15.4 L^{
}

Question 7.

A lead pencil consists of a cylinder of wood with a solid cylinder of graphite filled in the interior. The diameter of the pencil is 7 mm and the diameter of the graphite is 1 mm. If the length of the pencil is 14 cm, then find the volume of the wood and that of the graphite.

Solution.

Given, diameter of the graphite cylinder

^{
}

Question 8.

A patient in a hospital is given soup daily in a cylindrical bowl of diameter 7 cm. If the bowl is filled with soup to a height of 4 cm, then how much soup the hospital has to prepare daily to serve 250 patients?

Solution.

Given, diameter of bowl = 7 cm

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