#### Question

A farmer connects a pipe of internal diameter 20 cm form 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?

#### Solution

Consider an area of cross-section of pipe as shown in the figure.

Radius (*r*_{1}) of circular end of pipe = 20/200 = 0.1 m

Area of cross-section = `pixxr_1^2 = pixx(0.1)^2 = 0.01pi m^2`

Speed of water = 3 km/h = 3000/60 = 50 meter/min

Volume of water that flows in 1 minute from pipe = 50 × 0.01 π = 0.5π m^{3}

Volume of water that flows in *t* minutes from pipe = *t* × 0.5π m^{3}

Radius (*r*_{2}) of circular end of cylindrical tank = 10/2 = 5m

Depth (*h*_{2}) 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 ×(*r*_{2})^{2} ×*h*_{2}

*t* × 0.5 = 5^{2} ×2

*t* = 100

Therefore, the cylindrical tank will be filled in 100 minutes.