A farmer connects a pipe of internal diameter 25 cm from a canal into a cylindrical tank in his field, which is 12m in diameter and 2.5 m deep. If water flows through the pipe at 3.6 km/hr, in how much time will the tank be filled?

The cross-section of the pipe can be seen to have a cylindrical shape. As a result, the volume of water flowing at 3.6 km/hr, through the pipe to fill the tank is the same as the volume of water in the cylindrical tank.

Given : Radius of pipe $=12.5 \mathrm{cm}=0.125 \mathrm{m}$

Diameter of cylindrical tank $=12 \mathrm{m}$

Radius of Cylindrical tank $=6 m$

Height of Cylindrical tank $=2.5 \mathrm{m}$

 Volume of tank $=\pi {\text{r}}^2 \text{h}=\pi \times 6^2\times 2.5=90\pi {\text{m}}^3$

Speed of water $=3.6 \mathrm{km}/\mathrm{hr}$

In 1 hour, length of water column $=3.6 \mathrm{km}=3600 \mathrm{m}$

In 1 minute, length of water column $=3600/60 =60 \mathrm{m}$

Volume of water flowing through pipe in 1 minute = Volume of cylinder with radius $0.125 \text{m}$and height $60 \text{m}$

$60 \mathrm{m}=\pi {\mathrm{r}}^2 \mathrm{h}=\pi (0.125{)}^{2}60=\pi 0.9375{ \mathrm{m}}^3$

Time taken to fill the tank=Volume of tank/Volume of water flowing through pipe in 1 minute $=90\pi /\pi 0.9375=96$ minutes.