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

→Radius (r1) of circular end of pipe = 20/200 = 0.1m
→Area of cross-section = π × r1² = 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 = 5m
→Depth (h2) of cylindrical tank = 2m
→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 = πr2² × h2
→t × 0.5 = 5² × 2
→t = 25 × 2 / 0.5
→t = 100
Therefore, the cylindrical tank will be filled in 100 minutes.