Question

A hemispherical tank, full of water, is emptied by a pipe at the rate of 25/7 litres per second. How much time will it take to empty half the tank if the diameter of the base of the tank is 3 m?.

Answer 1

Volume of the tank $=\frac{2}{3}\pi r^3$

$=\frac{2}{3}\times \frac{22}{7}\times {\left(\frac{3}{2}\right)}^2$

$=\frac{99}{14}{m}^3$

$=\frac{99}{14}\times 1000litres$

$=\frac{99000}{14}litres$

Volume of water to be emptied $=\frac{1}{2}\times$ Volume of tank

$=\frac{1}{2}\times \frac{99000}{14}$

$=\frac{99000}{28}litres$

Time taken to empty $\frac{25}{7}litres=1sec$

Time taken to empty $1litres=\frac{7}{25}sec$

Time taken to empty $\frac{99000}{8}litres=\frac{7}{25}\times \frac{99000}{28}sec$

$=\frac{693000}{700}$

$=990sec$

$=\frac{990}{60}min$

$=16.5min$