Q. 93.9( 327 Votes )

A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in her field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled?

Answer :


As we know that 1m = 100cm
Therefore, 

Radius (r1) of circular end of pipe =

= 0.1 m


Area of cross-section =π × r12


= π × (0.1)2


= 0.01 π m2


Speed of water = 3 km/h


=


=


= 50 meter/min


The volume of water that flows in 1 minute from pipe = 50 × 0.01 π


= 0.5π m3


The volume of water that flows in t minutes from pipe = t × 0.5π m3


Radius (r2) of circular end of cylindrical tank =


= 5 m


Depth (h2) of cylindrical tank = 2 m


Let the tank be filled completely in t minutes


The volume of water filled in the tank in t minutes is equal to the volume of water flowed in t minutes from the pipe


The volume of water that flows in t minutes from pipe = Volume of water in the tank


t× 0.5π = π ×(r2)2 × h2


t× 0.5 = (5)2 ×2


t = 100


Hence, the cylindrical tank will be filled in 100 minutes.

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