A farmer connects a pipe of internal diameter 20 cm, from a canal into a cylindrical tank in his field, which is 10 m in diameter and 4 m deep. If water flows through the pipe a the rate of 5 km / hour, in how much time will the tank be filled?

Here, length of the pipe = h = 5 km = 5000 m

Diameter of the pipe = 20 cm

Thus, radius of the pipe = 10 cm = 0.1 m

Now, Volume of cylindrical pipe = πr²h

= π × 0.01 × 5000

= 50π m³

Therefore, volume of water that is flowing through the pipe at a rate of 5km/hr is 157.143 m³.

Now, height of the cylindrical tank = h’ = 4 m

Diameter of the cylindrical tank = d = 10 m

Thus, radius of the cylindrical tank = r = 5 m

Thus, volume of the cylindrical tank = πr ²h’

= π × 25 × 4 = 100π m³

As time required to fall 50π m³ of water in the tank = 1 hour

Thus, time required for 1m³ of water in the tank = (1/50π) hour

Thus, time required for 100π m³ of water to fall in the tank = = 2 hrs.

Therefore, 2 hours will be needed to fill the cylindrical tank.