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?

Formula:

Volume of cylinder = πr²h

Where r is base radius and h is height of the cylinder.

Let the time taken be ‘t’ hours.

Observe that, volume of water flowing through pipe will be equal to volume of water in cylindrical tank.

For pipe, we can consider

Radius = 1/2 × diameter = 10 cm = 0.1 m

Height = water flown in ‘t’ hours

⇒ Height = speed of water × time taken = ‘3t’ km = ‘3000t’ meters

For tank,

Radius = 1/2 × diameter = 5 m

Height = 2 m

∴ π(0.1)²(3000t) = π(5)²2