A farmer runs a pipe of internal diameter `20` cm from the canal into a cylindrical tank in his 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?

Explanation

Radius of the pipe, `r=10cm =(10/100)m=1/10m`.
Length of water flowing through the pipe in 1 hour,
h = 3 km = 3000 m.
Volume of water that flows through the pipe in 1 hour
`pir^(2)h=(pixx1/10xx1/10xx3000)m^(3)=(30pi)m^(3)`.
Radius of the cylindrical tank, R = 5 m.
.Depth of the tank, H = 2 m.
`"Volume of the tank "=piR^(2)H=(pixx5xx5xx2)m^(3)`
`=(50pi) m^(3)`
Time taken to fill the tank
`=("volume of the tank")/("volume of water flown in 1 hour"P)`
`=((50pi)/(30pi))"hours"=5/3"hours=1 hr 40 min".`
Hence, the required time is 1 hr 40 min.