Question

Water is flowing through a cylindrical pipe, of internal diameter $2cm$, into a cylindrical tank of base radius $40cm$, at the rate of $0.4m/s$. Determine the rise in level of water in the tank in half hours.

Answer 1

Volume of water flowing through pipe in $1$ secs

$=\pi R^{2}H=\pi \times 1^2\times 0.4\times 100{cm}^3$

Volume of water flowing through pipe in $30mins=30\times 60secs$

$=\pi \times 1^2\times 0.4\times 100\times 30\times 60$

Volume of cylindrical tank in $30mins$

$\pi \times {40}^2\times h=\pi r^{2}h$

$\Rightarrow \pi \times {40}^2\times h=\pi \times 1^2\times 0.4\times 100\times 30\times 60$

$\Rightarrow h=\frac{\pi \times 1^2\times 0.4\times 100\times 30\times 60}{\pi \times {40}^2}$

$=\frac{0.4\times 100\times 30\times 60}{40\times 40}=\frac{40\times 30\times 60}{40\times 40}=\frac{30\times 60}{40}=45cm$