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 $4m$ in diameter

Answer 1

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

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

$=\frac{99}{14}{m}^3$ ................ $v=\frac{2}{3}\pi r^3$

Volume of the water to be emptied $=\frac{1}{2}\times \frac{99}{14}{m}^3=\frac{99000}{28}litres$

Since $\frac{25}{7}$ litres of water is emptied in one second. therefore,
Total time taken to empty half the tank $\frac{99000}{28}$ litres of water

$=\frac{99000}{28}÷\frac{25}{7}seconds$

$=\frac{99000}{28}\times \frac{7}{25}$

$=\frac{99000}{28}\times \frac{7}{25}\times \frac{1}{60}mintes$

$=16.5minutes$