A cylindrical tank full of water is emptied by a pipe at the rate of 225 litres per minute. How much time will it take to empty half the tank, if the diameter of its base is $ 3 \mathrm{~m} $ and its height is $ 3.5 \mathrm{~m} $? [Use $ \pi=22 / 7] $.

Given:

A cylindrical tank full of water is emptied by a pipe at the rate of 225 litres per minute.

The diameter of its base is \( 3 \mathrm{~m} \) and its height is \( 3.5 \mathrm{~m} \).

To do:

We have to find the time it will take to empty half the tank.

Solution:

Diameter of the cylindrical tank $=3 \mathrm{~m}$

This implies,

Radius of the tank $r=\frac{3}{2} \mathrm{~m}$

Height of the tank $h=3.5 \mathrm{~m}$

$=\frac{7}{2} \mathrm{~m}$

Therefore,

Volume of the water filled in the tank $=\pi r^{2} h$

$=\frac{22}{7} \times \frac{3}{2} \times \frac{3}{2} \times \frac{7}{2}$

$=\frac{99}{4} \mathrm{~m}^{3}$
Volume of water in half the tank $=\frac{99}{4 \times 2} \mathrm{~m}^{3}$

$=\frac{99000}{8}$ litres.
Rate of flow of water $=225$ litres per min.

This implies,

Total time taken to empty the tank $=\frac{Volume}{Rate}$

$=\frac{99000}{8 \times 225}$

$=55$ minutes

It will take 55 minutes to empty half the tank.