Question

A hemispherical tank full of water is emptied by a pipe at the rate of $3\frac{4}{7}$ litres per second. How much time will it take to make the tank half-empty, if the tank is 3 m in diameter ?

Answer 1

Radius of hemispherical tank = $\frac{3}{2}m$

Therefore,

Volume of the tank = $\frac{2}{3}\times \frac{22}{7}\times (\frac{3}{2}{)}^3=\frac{99}{14}{m}^3$

Volume of the water to be emptied = $\frac{1}{2}\times \frac{99}{14}=\frac{99}{28}{m}^3$

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

Since, $\frac{25}{7}$ litres of water is emptied in one second. Therefore,

Total time taken to empty the half tank, i.e., $\frac{99000}{28}$ litres of water

$=\frac{99000}{28}\times \frac{7}{25}seconds=\frac{99000}{28}\times \frac{7}{25}\times \frac{1}{60}minutes=16.5minutes$