# Class 9 NCERT Solutions- Chapter 13 Surface Areas And Volumes – Exercise 13.6

Last Updated : 10 Mar, 2021

### 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 = 1l)

Solution:

Given values,

Circumference of the base of a cylindrical = 132 cm

Height of cylinder (h)= 25 cm

Base of cylinder is of circle shape, having circumference = 2Ï€r (r is radius)

Hence, 2Ï€r = 132 cm

r =                (taking Ï€=)

r =

r = 21 cm

So, volume of cylinder = Ï€r2h

= 22/7 Ã— 21 Ã— 21 Ã— 25                                 (taking Ï€=)

= 34650 cm3

As, 1000 cm3 = 1 litre

34650 cm3Ã— 34650

=

= 34.650 litres

### 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 of 0.6 g.

Solution:

Given values,

Inner radius of cylinder (r1)= = 12 cm

Outer radius of cylinder (r2)= = 14 cm

Height of cylinder (h)= 35 cm

So, volume used to make wood = volume of outer cylinder – volume of outer cylinder

= Ï€(r22)h – Ï€(r12)h

= Ï€(r22 – r12)h

Ã— (142 – 122) Ã— 35                     (taking Ï€=)

Ã— (52) Ã— 35

= 5720 cm3

As, 1 cm3 = 0.6 g

5720 cm3 = 0.6 Ã— 5720 g

= 3432 grams

= 3.432 kg

### Which container has greater capacity and by how much?

Solution:

Let’s see each case,

(i) The shape of can is cuboid here, as having rectangular base

Given values,

Length of can (l) = 5 cm

Width of can (b) = 4 cm

Height of can (h) = 15 cm

So, The amount of soft drink it can hold = volume of cuboid

= (l Ã— b Ã— h)

= 5 Ã— 4 Ã— 15 cm3

= 300 cm3

(ii)The shape of can is cylinder here, as having circular base

Given values,

Radius of can (r) = cm

Height of can (h) = 10 cm

So, The amount of soft drink it can hold = volume of Cylinder

= (Ï€r2h)

Ã— 10 cm3                                                  (taking Ï€=)

= 385 cm3

Hence, we can see the can having circular base can contain (385 – 300 = 85 cm3) more amount of soft drinks than first can.

### Question 4. If the lateral surface of a cylinder is 94.2 cm2 and its height is 5 cm, then find

(ii) its volume. (Use Ï€ = 3.14)

Solution:

Given values,

Lateral surface of cylinder = 94.2 cm2

Height of cylinder (h) = 5 cm

Let’s see each case,

(i) So, the lateral surface is of rectangle shape whose

length = (circumference of base circle of cylinder) and width = height of cylinder

Let the base radius = r

Lateral surface = length Ã— width

94.2 cm2 = (2Ï€r) Ã— h                         (circumference of circle = 2Ï€r)

94.2 cm2 = (2 Ã— 3.14 Ã— r) Ã— 5               (taking Ï€ = 3.14)

r =

r = 3 cm

(ii) Given values,

Radius of cylinder (r)= 3 cm

So, the volume of cylinder = (Ï€r2h)

= Ï€ Ã— 3 Ã— 3 Ã— 5 cm3

= 3.14 Ã— 3 Ã— 3 Ã— 5 cm3                    (taking Ï€ = 3.14)

= 141.3 cm3

### Question 5. It costs â‚¹2200 to paint the inner curved surface of a cylindrical vessel 10 m deep. If the cost of painting is at the rate of â‚¹20 per m2, find

(i) Inner curved surface area of the vessel,

(iii) Capacity of the vessel

Solution:

Given values,

Height of cylinder (h) = 10 m

Cost of painting rate = â‚¹20 per m2

Let’s see each case,

(i) For 1 m2 = â‚¹20

For lateral surface = â‚¹2200

So the lateral surface =

= 110 m2

(ii) Let the base radius = r

So as, Lateral surface = (circumference of base circle of cylinder) Ã— height

110 m2= (2Ï€r) Ã— h

110 = (2 Ã— Ã— r) Ã— 10               (taking Ï€=)

r = cm

r = cm

r = 1.75 cm

(iii) Volume of cylinder = (Ï€r2h)

Ã— 10 cm3                  (taking Ï€=)

= 96.25 cm3

### Question 6. The capacity of a closed cylindrical vessel of height 1 m is 15.4 liters. How many square meters of metal sheet would be needed to make it?

Solution:

Given values,

Height of cylinder (h) = 1 m = 100 cm

Volume of cylinder (V) = 15.4 liters

As 1 liter = 1000 cm3

15.4 liters = 15.4 Ã— 1000 cm3

V = 15,400 cm3

Volume of cylinder = (Ï€r2h)

15,400 = Ã— r2 Ã— 100                                       (taking Ï€=)

r2

r2 = 49

r = âˆš49

r = 7 cm

Surface area of a closed cylinder = (curve surface area + top and bottom circle) = 2Ï€rh + (2 Ã— Ï€r2)

= 2Ï€r (r+h)

= 2 Ã— Ã— 7 Ã— (7 + 100) cm2                                                   (taking Ï€=)

= 2 Ã— 22 Ã— 107

= 4708 cm2

= 0.4708 m2

Hence, 0.4708 m2 of metal sheet would be needed to make it.

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

Solution:

So here pencil = (cylinder of wood + cylinder of graphite)

Given values,

Height of wood (and graphite) cylinder (h) = 14 cm = 140 mm

Volume of Graphite = (Ï€r2h)

Ã— 140 mm3                                              (taking Ï€=)

= 110 mm3

= 0.11 cm3

Volume of wood = Volume of pencil – Volume of graphite

= (Ï€R2h) – (Ï€r2h) = Ï€(R2 – r2)h

Ã— (()2 – ()2) Ã— 140 mm3                                      (taking Ï€=)

= 22 Ã— 20 Ã— (– ) mm3

= 22 Ã— 20 Ã— 12 mm3

= 5280 mm3

= 52.80cm3

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

Solution:

So here Volume of soup for each patient = Volume of cylinder.

Given values,

Height of cylinder (h) = 4 cm

Volume of Cylinder = (Ï€r2h)

Ã— Ã— 4 cm3                                             (taking Ï€=)

= 154 cm

Volume of soup for 250 patient = 250 Ã— Volume of cylinder.

= 250 Ã— 154

= 38,500 cm3

Hence, 38,500cm3 soup is needed daily to serve 250 patients.

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