Question

A swimming pool $70m$ long, $44m$ wide and $3m$ deep, is filled by water issuing from a pipe of diameter $35cm$, at $6m/s$. How many hours does it take to fill the pool

Answer 1

We have, the given swimming pool in the form of the cuboid.

Given: dimensions of swimming pool $70m$ long, $44m$ wide, and $3m$ deep

diameter of pipe $=35cm=\frac{35}{100}m=35\times {10}^{-2}m$

Volume of Swimming pool $=l\times b\times h=70\times 44\times 3=9240m^3$

Volume of Water coming out from pipe in one sec

$=$ cross-section area of pipe $\times$ speed of water flowing in the pipe

$=\frac{22}{7}\times \frac{35}{2}\times {10}^{-2}\times \frac{35}{2}\times {10}^{-2}\times 6$

[$\because$ cross-section area of pipe $=\pi \times r^2$]

Time taken to fill the pool $=\frac{\text{Volume of Pool}}{\text{Volume of water coming out from pipe in one sec}}$

$=\frac{9240}{\frac{22}{7}\times \frac{35}{2}\times {10}^{-2}\times \frac{35}{2}\times {10}^{-2}\times 6}$

$=\frac{9240\times {10}^4}{\frac{11}{1}\times \frac{5}{1}\times \frac{35}{1}\times 3}$

$=\frac{9240\times {10}^4}{55\times 35\times 31}$

$=400\text{sec}=\frac{400}{60}minutes=6.67minutes$