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 of pipe (r₁) = 20 / 200 = 0.1 m
Area of cross- section of pipe = πr₁² = π(0.1)² = 0.01π m³
Speed of water = 3 km/h = 3000/60 = 50 m/min
Volume of water flows through in 1 minute = 50 × 0.01π = 0.5πm³
Volume of water flows through in t = t × 0.5π m³
Radius of cylindrical tank (r₂) = 5 m
Height of cylindrical tank (h₂) = 2 m
Let the tank will fill completely in t minutes.
Therefore,
The volume of water flows out in t minutes = volume of cylindrical tank
⇒ t × 0.5π = π ×(r₂)² ×h₂
⇒ t × 0.5 = 5² × 2
⇒ t = 100
Hence, the tank will completely fill in 100 minutes.