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Answer :
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.