Question

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

Answer 1

For the given tank.
Diameter = 10m
Radius of circular end of cylindrical tank, $R=\frac{10}{2}=5m$
Depth of cylindrical tank,$H=2m$
Internal radius of the pipe $=r=\frac{20}{2}cm=10cm=\frac{1}{10}m=0.1m$
Rate of flow of water $=v=3km/h=\frac{3000}{60}=50$ meter per minute
Let $t$ be the time taken to fill the tank.
So, the water flown through the pipe in t hours will equal to the volume of the tank
$\therefore \pi r^2\times v\times t=\pi R^{2}H$
$\Rightarrow {\left(0.1\right))}^2\times 50\times t=(5{)}^2\times 2$
$\Rightarrow t=\frac{25\times 2\times 100}{50}=100$
Hence,the cylindrical tank will be filled in $100$ min.