A hemispherical water tank has an internal radius of 21 m. It is full of water and is being emptied by a pump at a rate of 100 litres per second. How long will it take to drain the entire tank? (Use π = 22/7)

Solution

Solution: Volume of a hemisphere \(=\frac23\pi r^3\). Thus, \(V=\frac23\times\frac{22}{7}\times21^3=19404\text{ m}^3\). Converting to litres gives \(19,404,000\) litres. Time \(=\frac{19,404,000}{100}=194,040\) seconds. Converting to hours and minutes gives 53 hours and 54 minutes. Trick: Calculate the hemispherical volume in cubic metres, convert it to litres, and divide by the pump rate.