A farmer connects a pipe of internal diameter 20cm from a canal in to a
cylindrical tank to her field, which is 10m in diameter and 2m deep. If water
flows through the pipe at the rate of 3km/hr, in how much time will the tank be
filled?
Answers
ANSWER ⤵️
⇒Radius of circular end of pipe = 20/200 =0.1 m
⇒Area of cross-section =π×r 2/1 =π×(0.1)² =0.01π sq. m
⇒Speed of water =3 kilometer per hour = 3000/60=50 meter per minute.
⇒Volume of water that flows in 1 minute from pipe = 50×0.01π=0.5π cu. m
⇒From figure 2, Volume of water that flows in t minutes from pipe = t×0.5π cu. m
⇒Radius (r²) of circular end of cylindrical tank = 10/2=5 m
⇒Depth (h²) of cylindrical tank =2 m
⇒Let the tank be filled completely in t minutes.
⇒The volume of water filled in tank in t minutes is equal to the volume of water flowed in t minutes from the pipe.
⇒Volume of water that flows in t minutes from pipe = Volume of water in tank
Therefore, t×0.5π=πr2/2×h2
⇒t×0.5=5²×2
⇒t= 25×2/0.5
⇒t=100
Therefore, the cylindrical tank will be filled in 100 minute.