Question

The radius of a cylindrical cistern is 10 metres and its height is 15 metres. Initially the cistern is empty. We start filling the cistern with water through a pipe whose diameter is 50 cm. Water is coming out of the pipe at a velocity of 5 m/s. How many minutes will it take to fill the cistern with water?

Answer 1

Required time = \(\frac{\text{Volume of the cistern}}{\text{Volume of water coming out of the pipe in 1 second}}\)

= \(\frac{π\times10\times10\times15}{π\times\frac{0.5}{2}\times\frac{0.5}{2}\times5}\) seconds = \(\frac{200\times200\times15}{5\times5\times5}\) = 4800 seconds = \(\frac{4800}{60}\)min = 80 min.