In a rain-water harvesting system, the rain-water from a roof of $22\ m x 20\ m$ drains into a cylindrical tank having diameter of base 2 and height $3.5\ m$. If the tank is full, find the rainfall in cm. Write your views on water conservation.
Given: Roof size$=22\ m\times 20\ m$ and diameter of the base of cylindrical tank$=2\ m$ and height of the cylindrical tank$=3.5\ m$. The tank is full.
To do: To find the rainfall in cm.
Solution:
Let us say rainfall$=x\ cm$
roof size$=22\times 20$
volume of the water collected on the roof$=\frac{( 22\times 20) x}{100} \ \ m^{3} \ \ \ \ \ \ \left( \because x\ cm=\frac{x}{100} \ m\right)$
Diameter of the tank$=2\ m$
$\therefore$ Radius of the tank,$r=\frac{diameter}{2} =\frac{2}{2} =1\ m$
Height of the tank, $h=3.5\ m$
volume of the cylinderical tank$=\pi r^{2} h$
$=\frac{22}{7} \times ( 1)^{2} \times 3.5$
$=11\ m^{3}$
$\because$ Total water from the roof flown to the tank through drain pipe.And the tank is full.
volume of water collected on roof$=$volume of the tank
$\frac{( 22\times 20) x}{100} =11$
$\Rightarrow x=\frac{11\times 100}{22\times 20} =2.5\ cm$
Thus, The rainfall is $2.5\ cm$.
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