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Question
A cylindrical water tank has a diameter 4 m and is 6 m high. Water is flowing into it from a cylindrical pipe of diameter 4 cm at the rate of 10 m/s. In how much time the tank will be filled?
Solution
For the cylindrical tank:
diameter = 4m
radius
= 2m
= 200m
Height
= 6m
= 600cm
Volume of the cylindrical tank
= π2h
= π(200)2 x 600
= 2400000πcm3
For the cylindrical pipe:
diameter = 4cm
radius = 2cm
rate of flow water
= 10m/s
= 100cm/s
Volume of water flown in 1 sec
= area of base x rate of flow of water
= πx 22 x1000
= 4000πcm3
∴ Time takken to fill the tank
= `(24000000pi)/(4000pi)`
= `(24000)/(4)`
= 6000 s
= `(6000)/(60)"mins"`
= 100minutes
∴ The time taken to fill the tank is 100mins.
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