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 km/h, in how much time will the tank be filled?
Radius (r1) of circular end of pipe =
= 0.1 m
Area of cross-section =π * r12
= π * (0.1)2
= 0.01 π m2
Speed of water = 3 km/h
=
=
= 50 meter/min
Volume of water that flows in 1 minute from pipe = 50 × 0.01 π
= 0.5π m3
Volume of water that flows in t minutes from pipe = t × 0.5π m3
Radius (r2) of circular end of cylindrical tank =
= 5 m
Depth (h2) of cylindrical tank = 2 m
Let the tank be filled completely in t minutes
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
t× 0.5π = π ×(r2)2 ×h2
t× 0.5 = (5)2 ×2
t = 100
Hence, the cylindrical tank will be filled in 100 minutes