Question

A hemispherical tank full of water is emptied by a pipe at the rate of 25/7 litres per second. How much time will it take to empty half the tank, if it is 3m in diameter? (Take $\pi =\frac{22}{7}$)

Answer 1

Given,
Diameter of the hemispherical tank$=3m$
So, radius $=\frac{d}{2}$$=\frac{3}{2}m$

Volume of the tank

$=\frac{2}{3}\pi r^2$

$=\frac{2}{3}\times \frac{22}{7}\times {\left(\frac{3}{2}\right)}^3{m}^3=\frac{99}{14}{m}^3$

So, the volume of the water to be emptied

$=\frac{1}{2}\times \frac{99}{14}=\frac{99}{28}\times 1000litres$ $(1m^3=1000litre$)

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

Since, $\frac{25}{7}$ litres of water is emptied in 1 second

Therefore $\frac{99000}{28}$ litres of water will be emptied in

$=\frac{99000}{28}\times \frac{7}{25}=\frac{3960}{4}=990Sec.$ .
i.e., $\frac{990}{60}=16.5$ minutes