A hemispherical tank full of water is emptied by a pipe at the rate of 7.7 litres per second. How much time (in hours) will it take to empty $$\frac{2}{3}$$ part of the tank, if the internal radius of the tank is 10.5 m?

Solution (By Examveda Team)

$$\eqalign{ & 7.7{\text{ Ltr/sec}} \cr & r = 10.5{\text{ cm}} \cr & {\text{V}} = \frac{2}{3}\pi {r^3} \times \frac{2}{3} \cr & = \frac{{\frac{2}{3} \times \frac{2}{3} \times \frac{{22}}{7} \times 10.5 \times 10.5 \times 10.5 \times 1000}}{{7.7 \times 60 \times 6000}} \cr & = \frac{{20 \times 105}}{{36}} \cr & = \frac{{175}}{3}{\text{ hours}} \cr} $$