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

Diameter of the pipe = 20 cm

$$\therefore$$ Radius of the pipe = 10 cm

Length of water column per hour
= 3 km = 3 × 1000 × 100 cm

Volume of water flown in one hour
$$= \ \pi \ × \ 100 \ × \ 300000$$ cm3

Tank to be filled = Volume of cylinder
(with r = 5m = 500 cm and h = 2m = 200 cm)

$$= \ \pi \ × \ 500 \ × \ 500 \ × \ 200$$ cm3

Time required to fill the tank
$$= \ \frac{Volume \ of \ tank}{Volume \ of \ water \ flown}$$

$$= \ \frac{ \pi \ × \ 500 \ × \ 500 \ × \ 200}{ \pi \ × \ 100 \ × \ 300000}$$

$$= \ \frac{5}{3} \ = \ 100$$ minutes.