Question

Water is being pumped out through a circular pipe whose diameter is p cm. If the flow of water is 14p cm per second, how many liters of water are being pumped out in one one hour? (Take $\pi =\frac{22}{7}$ )

Answer 1

A circular pipe with water flowing in it is a solid cylinder.

According to question, flow of water in the pipe is $14p$ cm/sec.

In one second, length of water column in the pipe is $14p$ cm, and the diameter of pipe is $p$ cm.

Volume of water in the pipe in one second $=$ Volume of cylinder$=\pi r^{2}l$,

where $r=$ radius of cylinder $=$ Diameter of cylinder $÷2=p÷2=\frac{p}{2}cm$

and $l=$ length of cylinder$=14p$

Thus, Volume of water in the pipe in one hour $=3600\times$Volume of water in the pipe in one second.

$V=3600\times \pi \times (\frac{p}{2}{)}^2\times 14p$

$\Rightarrow V=3600\times \frac{22}{7}\times \frac{p^2}{4}\times 14p=39600p^{3}c{m}^3$

Since, $1c{m}^3=\frac{1}{1000}L$

$\therefore Volume=39600p^3\times \frac{1}{1000}L=39.6p^{3}L$