Question

A farmer connects a pipe of internal diameter 20 cm from a canal into a cylindrical tank is her 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

Internal diameter of a pipe = 20 cm
Radius of pipe = 10 cm = $\frac{1}{10}m$
Diameter of cylindrical tank = 10 m; r = 5 m
Depth of cylindrical tank = 2 m
Speed of water is 3 km/hr
Time required to fill the water tank = ?
Speed of water = 3 km/hr
$=\frac{3000}{60}$ m/minute
$=50$ m/min
Let time required to fill the tank be 'n' minutes
$\therefore$ Flowing water in 'n' minutes = Volume of water tank
$\Rightarrow \pi \times (\frac{1}{10}{)}^2\times (n\times 50)=\pi \times (5{)}^2\times 2$
$\frac{1}{100}n\times 50=50$
$\therefore n=100$ minutes
$\therefore$ Time required to fill the water tank = 100 minutes