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RD Chapter 19 Surface Areas and Volume of a Circular Cylinder Ex 19.2 Solutions

Question - 21 : - From a tap of inner radius 0.75 cm, water flows at the rate of 7 m per second. Find the volume in litres of water delivered by the pipe in one hour.

Answer - 21 : - Inner radius of a tap = 0.75 cm
Speed of flow of water in it = 7 m/s
Time = 1 hour
∴ Length of flow of water(h)
= 7 x 60 x 60 m = 25200 m
∴ Volume of water = πr2h

Question - 22 : - A rectangular sheet of paper 30 cm x 18 cm can be transformed into the curved surface of a right circular cylinder in two ways i.e., either by rolling the paper along its length or by rolling it along its breadth. Find the ratio of the volumes of the two cylinders thus formed.

Answer - 22 : - Size of rectangular sheet = 30 cm x 18 cm
∴ Length of sheet = 30 cm
and breadth = 18 cm
By folding length wise,
Height = 18 cm
and circumference = 30 cm

Question - 23 : - How many litres of water flow out of a pipe having an area of cross-section of 5 cm2 in one minute, if the speed of water in the pipe is 30 cm/sec?

Answer - 23 : - Area of the cross-section of the pipe = 5 cm2
Speed of water flow = 30 cm/sec
Period = 1 minute
∴ Flow of water in 1 minute= 30 x 60 cm = 1800 cm
Area of mouth of pipe = 5 cm2
∴ Volume = 1800 x 5 = 9000cm3
Volume of water in litres = 9000 ml

Question - 24 : - Find the cost of sinking a tubewell 280 m deep, having diameter 3 m at the rate of ₹3.60 per cubic metre. Find also the cost of cementing its inner curved surface at ₹2.50 per square metre.

Answer - 24 : - Depth of well (h) = 280 m
Diameter = 3 m

Question - 25 : - Find the length of 13.2 kg of copper wire of diameter 4 mm, when 1 cubic cm of copper weighs 8.4 gm.

Answer - 25 : - Weights of copper wire = 13.2 kg
Diamter = 4 mm

Question - 26 : - A solid cylinder has a total surface area of 231 cm2.Its curved surface area is 2/3 of the total surface area. Find the volume ofthe cylinder.

Answer - 26 : - Surface area of solid cylinder = 231 cm2
and curved surface area = 2/3 of 231 cm2

Question - 27 : - 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 a width of 21 m to form an embankment. Find the height of the embankment.

Answer - 27 : - Diameter of a well = 14 m
∴ Radius (r) = y = 7 m
Depth (h) = 8 m
∴ Volume of the earth dugout= πr2h

Question - 28 : - The difference between inside and outside surfaces of a cylindrical tube 14 cm long is 88 sq. cm. If the volume of the tube is 176 cubic cm, find the inner and outer radii of the tube.

Answer - 28 : - Length of cylindrical tube = 14 cm
Difference betveen the outer surface and inner surface = 88 cm2
and volume of the tube = 176 cm3
Let R and r be the outer and inner radius of the tube

Question - 29 : - Water flows out through a circular pipe whose internal diameter is 2 cm, at the rate of 6 metres per second into a cylindrical tank. The radius of whose base is 60 cm. Find the rise in the level of water in 30 minutes?

Answer - 29 : - Internal diameter of the pipe = 2 cm
∴ Radius (r) = 2/2 = 1 cm
Speed of water flow = 6m per second Water in 30 minutes (h) = 6 x 60 x 30 m =10800 m
Volume of water = πr2h

Question - 30 : - A cylindrical water tank of diameter 1.4 m and height 2.1 m is being fed by a pipe of diameter 3.5 cm through which water flows at the rate of 2 metre per second. In how much time the tank will be filled?

Answer - 30 : - Diameter of cylindrical tank = 1.4 m
∴ Radius (r) = 1.4/2 = 0.7 m
and height (h) = 2.1 m
∴ Volume of water in thetank = πr2h

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