Question

A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank in his field, which is 10 m in diameter and 2 m deep. If water flows through the pipe at the rate of 3 km/h, in how much time will the tank be filled?

Answer 1

Radius of pipe = 10 cm = 0.1 m,
Rate of water flow = 3000 m/h
Radius of tank = 5 m, depth = 2 m

Volume of water that flows through the pipe in 1 hr
$=\pi r^{2}h$
$=\pi \times {0.1}^2\times 3000$
$=30\pi \frac{m^3}{h}$

Volume of tank
$=\pi r^{2}h$
$=\pi \times 5^2\times 2$
$=50\pi m^3$

$\Rightarrow \text{Time taken to fill the tank}=\frac{\text{Volume of tank}}{\text{Volume of water in 1hr}}$
$=\frac{50\pi }{30\pi }=1hr67min$