Question

Water is flowing at the rate of $15km$ per hour through a pipe of diameter $14cm$ into a rectangular tank which is $50m$ long and $44m$ wide. Find the time in which the level of water in the tank will rise by $21cm$.

Answer 1

Let the length of the pipe for filling the whole tank be $h$ m.

(i) pipe is in the form of cylinder where height $=hm$

diameter $=14cm$

$\Rightarrow =\frac{14}{2}=7cm=\frac{7}{100}m$

Volume of pipe $=$ volume of cylinder $=\pi r^{2}h$

$\Rightarrow \pi r^{2}h=\pi {\left(\frac{7}{100}\right)}^{2}h=\frac{22}{7}\times \frac{7}{100}\times \frac{7}{100}\times h=\frac{22\times 7h3}{100\times 100}$

(ii) Tank is in the form of caloid where $l=500m$

$b=44m,h=21cm=\frac{21}{100}m=0.21m$

Volume of the tank $=lbh=50\times 44\times \frac{21}{100}=22\times 21m^2$

We have volume of pipe $=$ volume of tank

$\Rightarrow \frac{22\times 7h}{100\times 100}=22\times 21$

$\Rightarrow h=3\times 10000m=\frac{30,000}{1000}km=30km$

Water in pipe flows at the rate of $15km/hr$

$30km$ travels in pipe in $\frac{30}{15}hrs=2hrs$

So, in $2$hrs, the tank will be filed.