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NCERT Solutions for Class 9th Mathematics

 

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Chapter 13. Surface Areas and Volumes

Exercise 13.6

 

 

 

EXERCISE 13.6

Assume π = 22/7, unless stated otherwise.

Q1. The circumference of the base of a cylindrical vessel is 132 cm and its height is 25 cm. How many litres of water can it hold? (1000 cm3 = 1 l)

Solution:

Circumference of cylinder = 132 cm

Height = 25 cm

2πr = 132 cm

Q2. 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 of 0.6 g.

Solution:

Inner radius = 24 cm

Outer radius = 28 cm

(i) volume of inner cylinder = πr2h

110 × 196

21560 cm3

Total volume = v1 + v2

⇒ 15840 + 21560 cm3

37400 cm3

Mass = 37400 × 0.6

22440

Q3. 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:

Length = 5cm, breadth = 4cm, height = 15cm

Diameter = 7cm, height = 10cm, r = 3.5cm

Volume of cuboid = l × b × h

5 × 4 × 15 cm

20 × 15 cm

300 cm3

Volume of cylinder = πr2h

 × 3.5 × 3.5 × 10

22 × 5 × 3.5

110 × 3.5

385 cm3

Capacity of both

300 cm=  385 cm3

385 – 300

85 cm3

Q4. If the lateral surface of a cylinder is 94.2 cm2 and its height is 5 cm, then find

(i) radius of its base       (ii) its volume. (Use  = 3.14)

Solution:

Height = 5 cm

Lateral surface area of the cylinder = 2πrh

2 × 3.14 × r × 5 = 94.2 cm2

Q5. It costs 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:

Cost = Rs. 2200

Height = 10 m

Q6. The capacity of a closed cylindrical vessel of height 1 m is 15.4 litres. How many square metres of metal sheet would be needed to make it?

Solution:

Height = 1 m

Capacity = 15.4 l

Q7. 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, find the volume of the wood and that of the graphite.

Solution:

Q8. 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, how much soup the hospital has to prepare daily to serve 250 patients?

Solution:

 

 

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