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 half empty the tank, if the tank is $3$ metres in diameter? (Take $\pi =\frac{22}{7})$

• A. $16.5$ min.
• B. $12.8$ min.
• C. $20.5$ min.
• D. $18.2$ min.

Answer 1

The correct option is A $16.5$ min.

Radius of the hemispherical tank $=\frac{3}{2}=1.5$ m

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

Hence, volume of the tank $=\frac{2}{3}\times \frac{22}{7}\times \frac{3}{2}\times \frac{3}{2}\times \frac{3}{2}=\frac{99}{14}{m}^3$

Half of the volume of the tank $=\frac{99}{28}{\text{m}}^3=\frac{99}{28}\times 1000$ litres

To empty, $3\frac{4}{7}=\frac{25}{7}$ litres, time is one second

To empty $\frac{99}{28}\times 1000$ litres, time $=\frac{\frac{99}{28}\times 1000}{\frac{25}{7}}=990$ seconds $=16.5$ min