Question

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

Answer 1

Let length of the pipe for filling the whole tank be km/h

volume of pipe volume of tank

pipe is in form of cylinder where

Height $=$ h

Diameter $=20$cm

Radius $=\frac{20}{2}cm=\frac{1}{10}m$

$Volumeofpipe=volumeofcylinder$

$=\pi r^{2}h$

$=\frac{\pi h}{100}$

volume of tank

Diameter $=10m$ i.e., Radius $=5m$

Height$=2m$

volume of tank $=\pi r^{2}h=\pi \times 25\times 2=50\pi$

Now,

volume of tank = volume of pipe

$50\pi =\frac{\pi h}{100}$

$h=5000m$

$h=5km$

Water in pipe flows at $3$ km\h

So $3$ km travels in $1$ hour

$1km$ in $\frac{1}{3}hr$

$5km$ in pipe $=\frac{5}{3}hr$

$=\frac{5}{3}\times 60min$

$=100min$

So, in $100min$ tank will be filled.