Question

A hemispherical tank, of diameter 3 m, is full of water. It is being emptied by a pipe at the rate of \[3\frac{4}{7}\] litre per second. How much time will it take to make the tank half empty?\[\left[ Use \pi = \frac{22}{7} \right]\]

 

Answer 1

Radius of the hemispherical tank =\[\frac{3}{2} m\]

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

So,

Amount of water to be taken out of the tank =\[\frac{1}{2} \times \frac{99}{14} m^3 = \frac{99}{28} \times 1000 litres = \frac{99000}{28} L\]

Since \[\frac{25}{7}\] litres of water is taken out in 1 second,

\[\frac{99000}{28}\] litres of water will be taken out in\[\frac{99000}{28} \times \frac{7}{25}\] seconds, i.e. 16.5 minutes.