Question

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?​

Answer 1

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.