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

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 cm³ = 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 cm³ 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 cm³ …(i)

Question 4.
If the lateral surface area of a cylinder is 94.2 cm² 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 cm²
∴ 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 = πr²h = 3.14 x (3)² x 5
= 3.14 x 9 x 5 = 141.3cm³

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 m², 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 m²
(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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