Question

A cylindrical pipe has inner diameter of $4$ cm and water flows through it at the rate of $20$ per minute. How long would it take to fill a conical tank of radius $40$ cm and depth $72$ cm?

Answer 1

We have

Diameter of base of conical vessel $=80cm$

so, radius $=40cm$

and, Height of the conical vessel $72cm$

Thus volume of conical vessels $=\pi r^2\frac{h}{3}$

$=\pi \times {\left(40\right)}^2\times \frac{72}{3}$

$=\pi \times 40\times 40\times 24$

$=38400\pi c{m}^3---\left(1\right)$

Let the conical vessel is filled in $x$ min than length of water column $=200xm$

So, length of the cylinder $=2000xcm$

and diameter of pipe $=4cm$

Now,

Volume of water flows in $x$ minutes $=\pi \times {\left(2cm\right)}^2\times 20000cm$

$=8000\pi xc{m}^3----\left(2\right)$

Equating $\left(1\right)$ and $\left(2\right)$ we get

$38400\pi =8000\pi x$

$x=4min48sec$

Hence, which is the required answer.