A hemispherical tank full of water is emptied by a pipe

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

$=\frac{33}{2}$

$=16.5 \mathrm{~min} .$