# RD SHARMA Solutions for Class 9 Maths Chapter 19 - Surface Areas and Volume of a Circular Cylinder

## Chapter 19 - Surface Areas and Volume of a Circular Cylinder Exercise 19.28

In a cylinder, if radius is doubled and height is halved, curved surface area will be

(a) halved

(b) doubled

(c) same

(d) four times

Two cylindrical jars have their diameters in the ratio 3 : 1, but height 1 : 3. Then the ratio of their volumes is

(a) 1 : 4

(b) 1 : 3

(c) 3 : 1

(d) 2 : 5

The number of surfaces in right cylinder is

(a) 1

(b) 2

(c) 3

(d) 4

Number of Surfaces In a Right cylinder are 3.

Top surface, bottom surface and curved surface.

Hence, correct option is (c).

Vertical cross-section of a right circular cylinder is always a

(a) square

(b) rectangle

(c) rhombus

(d) trapezium

Vertical cross-section of cylinder will always be a Rectangle of sides 'h', and 'r',

where h is the height of a cylinder and r is the radius of a cylinder.

Hence, correct option is (b).

If r is the radius and h is height of the cylinder the volume will be

Volume of cylinder

= Area of Base × Height

= (∏r^{2}) × h

V = ∏r^{2}h

Hence, correct option is (b).

The number of surfaces of a hollow cylindrical object is

(a) 1

(b) 2

(c) 3

(d) 4

A Hollow cylinder has only 2 surfaces.

One is outer-curved surface and another is inner-curved surface.

Hence, correct option is (b).

## Chapter 19 - Surface Areas and Volume of a Circular Cylinder Exercise 19.29

If the radius of a cylinder is doubled and the height remains same, the volume will be

(a) doubled

(b) halved

(c) same

(d) four times

Volume of a cylinder = V = ∏r^{2}h

If r' = 2r and h' = h, then

V' = ∏(2r)^{2}h = 4∏r^{2}h

V' = 4V

Hence, correct option is (d).

If the height of a cylinder is doubled and radius remains the same, then volume will be

(a) doubled

(b) halved

(c) same

(d) four times

Volume of cylinder V = ∏r^{2}h

If h' = 2h and r' = r, then

V' = ∏(r)^{2}(2h) = 2∏r^{2}h = 2V

Hence, correct option is (a).

In a cylinder, if radius is halved and height is doubled, the volume will be

(a) same

(b) doubled

(c) halved

(d) four times

If the diameter of the base of a closed right circular cylinder be equal to its height h, then its whole surface area is

A right circular cylindrical tunnel of diameter 2 m and length 40 m is to be constructed from a sheet of iron. The area of the iron sheet required in m^{2}, is

(a) 40∏

(b) 80∏

(c) 160∏

(d) 200∏

Two circular cylinders of equal volume have their heights in the ratio 1 : 2. Ratio of their radii is

The radius of a wire is decreased to one-third. If volume remains the same, the length will become

(a) 3 times

(b) 6 times

(c) 9 times

(d) 27 times

If the height of a cylinder is doubled, by what number must the radius of the base be multiplied so that the resulting cylinder has the same volume as the original cylinder?

The volume of a cylinder of radius r is 1/4 of the volume of a rectangular box with a square base of side length x. If the cylinder and the box have equal heights, what is r in terms of x?

The height h of a cylinder equals the circumference of the cylinder. In terms of h, what is the volume of the cylinder?

A cylinder with radius r and height h is closed on the top and bottom. Which of the following expressions represents the total surface area of this cylinder?

(a) 2∏r (r + h)

(b) ∏r (r + 2h)

(c) ∏r (2r + h)

(d) 2∏r^{2 }+ h

Total surface Area = Area of Top + Area of bottom + Curved Surface Area

T.S.A. = ∏r^{2} + ∏r^{2} + 2∏rh = 2∏r^{2} + 2∏rh = 2∏r (r + h)

Hence, correct option is (a).

## Chapter 19 - Surface Areas and Volume of a Circular Cylinder Exercise 19.30

The height of sand in a cylindrical-shaped can drops 3 inches when 1 cubic foot of sand is poured out. What is the diameter, in inches, of the cylinder?

Two steel sheets each of length a_{1} and breadth a_{2} are used to prepare the surfaces of two right circular cylinders - one having volume v_{1} and height a_{2} and other having volume v_{2} and height a_{1}. Then,

(a) v_{1} = v_{2}

(b) a_{1}v_{1} = a_{2}v_{2}

(c) a_{2}v_{1} = a_{1}v_{2}

(d)

The altitude of a circular cylinder is increased six times and the base area is decreased one-ninth of its value. The factor by which the lateral surface of the cylinder increases, is

## Chapter 19 - Surface Areas and Volume of a Circular Cylinder Exercise Ex. 19.1

^{2}. If the radius of the base of the cylinder is 0.7 m, find its height.

Radius (r) of circular end of pipe = cm = 2.5 cm = 0.025 m

CSA of cylindrical pipe = = 4.4

Thus, the area of radiating surface of the system is 4.4 m

^{2}or 44000 cm

^{2}.

^{2}.

Radius of the circular end of the pillar = cm = 25 cm = 0.25 m

CSA of pillar = =

Cost of painting 1 area = Rs 12.50

Cost of painting 5.5 area = Rs (5.5 12.50) = Rs 68.75

Thus, the cost of painting the CSA of pillar is Rs 68.75.

Base radius (r) of cylindrical tank = = 70 cm = 0.7 m

Area of sheet required = total surface area of tank =

So, it will require 7.48 of metal sheet.

The inner diameter of a circular well is 3.5 m. It is 10 m deep. Find

(ii) The cost of plastering this curved surface at the rate of Rs 40 per m

^{2}

Depth (h) of circular well = 10 m

= (44 x 0.25 x 10)

= 110 m

^{2}

^{2}area = Rs 40

Cost of plastering 110 m

^{2}area = Rs (110 x 40) = Rs 4400

Height of penholder = 10.5 cm

Surface area of 1 penholder = CSA of penholder + Area of base of

Area of cardboard sheet used by 1 competitor =

Area of cardboard sheet used by 35 competitors

= 7920 cm2

Thus, 7920 cm

^{2}of cardboard sheet will be required for the competition.

Twenty cylindrical pillars of the Parliament House are to be cleaned. If the diameter of each pillar is 0.50 m and height is 4 m. What will be the cost of cleaning them at the rate of Rs 2.50 per square metre?

The total surface area of a hollow metal cylinder open at both ends of external radius 8 cm and height 10 cm is 338 cm^{2}. Taking r to be inner radius, obtain an equation in r and use it to obtain the thickness of the metal in the cylinder.

Find the lateral or curved surface area of a cylindrical petrol storage tank that is 4.2 m in diameter and 4.5 m high. How much steel was actually used, if of the steel actually used was wasted in making the closed tank?

Radius (r) of circular end of cylindrical tank =m = 2.1m

(i) Lateral or curved surface area of tank =

=

= 59.4 m2

(ii) Total surface area of tank = 2 (r + h)

=

= 87.12 m

^{2}

Let A m

^{2}steel sheet be actually used in making the tank.

Thus, 95.04 steel was used in actual while making the tank.

## Chapter 19 - Surface Areas and Volume of a Circular Cylinder Exercise Ex. 19.2

(i) a tin can with a rectangular base of length 5 cm and width 4 cm, having a height of 15 cm and

Breadth (b) of tin can = 4 cm

Height (h) of tin can = 15 cm

Capacity of tin can = l b h = (5 4 15) cm

^{3}= 300 cm

^{3}

^{2}H ==385 cm

^{3}

Difference in capacity = (385 - 300) cm

^{3}= 85 cm

^{3}

^{3}of wood has a mass of 0.6 g.

^{2}and its height is 5 cm, then find

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

Let radius of cylinder be r.

CSA of cylinder = 94.2 cm

^{2}

2rh = 94.2 cm

^{2}

(2 3.14 r 5) cm = 94.2 cm

^{2}

r = 3 cm

^{2}h = (3.14 (3)

^{2}5) cm

^{3}= 141.3 cm

^{3}

Height (h) of the cylindrical vessel = 1 m

Volume of cylindrical vessel = 15.4 litres = 0.0154 m

^{3}

^{}

^{2}of metal sheet would be needed to make the cylindrical vessel.

Height (h) up to which the bowl is filled with soup = 4 cm

^{2}h=

Volume of soup in 250 bowls = (250 154) cm

^{3}= 38500 cm

^{3}= 38.5 litres

Thus, the hospital will have to prepare 38.5 litres of soup daily to serve 250 patients.

A cylinderical container with diameter of base 56 cm contains sufficient water to submerge a rectangular solid of iron with dimensions 32 cm x 22 cm x 14 cm. Find the rise in the level of the water when the solid is completely submerged.

A well with 14 m diameter is dug 8 m deep. The earth taken out of it has been evenly spread all around it to around it to a width of 21 m to form an embankment. Find the height of the embankment.

Water flows out through a circular pipe whose internal diameter is 2 cm, at the rate of 6 meters per second into cylindrical tank. The water is collected in a cylindrical vessel radius of whose base is 60 cm. Find the rise in the level of water in 30 minutes?

The sum of the radius of the base and height of a solid cylinder is 37 m. If the total surface area of the solid cylinder is 1628 m^{2}. Find the volume of the cylinder.

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