A hemispherical tank of internal radius 10.5 m is full of water. It is emptied by a pipe at the rate of 7.7 litres per second. How much time will it take to empty one-third of the tank? (Take \(\pi=\frac{22}{7}\))
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → \(\displaystyle\frac{175}{6}\) hours
The volume of a hemisphere of radius \(r\) is \(\displaystyle\frac{2}{3}\pi r^3\), and 1 m3 \(=1000\) litres. Time \(=\) volume \(\div\) rate.
Volume of the tank \(\displaystyle=\frac{2}{3}\times\frac{22}{7}\times10.5\times10.5\times10.5=2425.5\) m3
One-third of it \(=2425.5\div3=808.5\) m3 \(=8{,}08{,}500\) litres
Time \(=808500\div7.7=105000\) seconds
In hours: \(\displaystyle\frac{105000}{3600}=\frac{175}{6}\) hours