Question

A cylindrical tank full of water is emptied by a pipe at the rate of 225 litres per minute. How much time will it take to empty half the tank, if the diameter of its base is 3 m and its height is 3.5 m? [Use $\mathrm{\pi }=\frac{22}{7}$] [CBSE 2014]

Answer 1

Volume of cylidrical tank = $\frac{22}{7}\times {\left(\frac{3}{2}\right)}^2\times 3.5$ = 24.75 m³
Now, 1 m³ = 1000 L
∴ 24.75 m³ = 24750 L
Half the capacity of tank = 12375 L

Time taken by the pipe to empty 225 litres = 1 minute
Time taken by the pipe to empty 1 litre = $\frac{1}{225}$ minutes
Time taken by the pipe to empty 12375 litres = $\frac{1}{225}\times 12375=55\mathrm{minutes}$