Q19 of 47 Page 1

A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank which is 10 m in diameter and 2 m deep. If the water flows through the pipe at the rate of 4 km per hour, in how much time will the tank be filled completely?

Diameter of cylindrical tank, D = 10m


Radius of cylindrical tank, R = 5m


Depth of cylindrical tank, H = 2m


Internal diameter of cylindrical pipe, d = 20 cm


We know that 1m = 100cm.


Internal radius of cylindrical pipe, r = 10cm = 1/10 m


We know that 1km = 1000m.


Rate of flow of water, v = 4 km/h = 4000 m/h


Let t be the time taken to fill the tank completely.


Water flowed through the pipe = Volume of the cylindrical tank


So, πr2v × t = πR2H


⇒ π(1/10)2 (4000)t = π(5)2(2)


⇒ t = 5/4


Converting into minutes,


⇒ t = 5(60)/4


⇒ t = 75 mins


Ans. The tank will be filled completely in 75 minutes.


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