Question

A hemispherical tank is emptied by a pipe at the rate of $5$ litres per minute. How long will it take to half-empty the tank if its diameter is $1\frac{1}{2}m$.

Answer 1

Diameter of the hemispherical tank $=1\frac{1}{2}=\frac{3}{2}m$

Radius $=\frac{\frac{3}{2}}{2}=\frac{3}{4}m$

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

$=\frac{2}{3}\times \frac{22}{7}\times (\frac{3}{4}{)}^3=\frac{99}{112}{m}^3$

Volume of water that would be emptied $=\frac{1}{2}$ of volume of hemispherical tank

$=\frac{1}{2}\times \frac{99}{112}=\frac{99}{224}{m}^3$

$=\frac{99}{28}\times 1000$ litres [$\because 1m^3=1000$ litres]

$=\frac{99000}{224}$ litres

A pipe can empty $5$ litres in $1$ minute.

so, the same pipe will empty $\frac{99000}{224}$ litres in $\frac{1}{5}\times \frac{99000}{224}=88.39$ minutes