Question:
A hemispherical tank full of water is emptied by a pipe at the rate of $\frac{25}{7}$ litres per second. How much time will it take to half-empty the tank, If the tank is 3 metres in diameter?
Solution:
Volume of half of hemispherical tank
$=\frac{2}{3} \pi r^{3}$
$=\frac{2}{3} \times \frac{22}{7} \times\left(\frac{3}{2}\right)^{3}$
$=\frac{49500}{7} \mathrm{ltr} .$
Amount of water emptied by pipe in $1 \mathrm{sec} .=\frac{25}{7} \mathrm{ltr}$.
So, time taken
$=\frac{7}{25} \times \frac{49500}{7}$
$=1980 \mathrm{sec} .$
$=\frac{1980}{60} \mathrm{~min}$
$=33 \mathrm{~min}$
To half empty the tank line
$=\frac{33}{2}$
$=16.5 \mathrm{~min} .$