The rain water from a roof of 44 m × 20 m drains into a cylindrical tank having diameter of base 4 m and height 3.5 m.

Solution:

We have,

the length of the roof, $l=44 \mathrm{~m}$,

the width of the roof, $b=20 \mathrm{~m}$,

the height of the cylindrical tank, $H=3.5 \mathrm{~m}$ and

the base radius of the cylindrical tank, $R=\frac{4}{2}=2 \mathrm{~m}$

Let the height of the rainfall be $h$.

Now,

Volume of rainfall $=$ Volume of cylindrical tank

$\Rightarrow l b h=\pi R^{2} H$

$\Rightarrow 44 \times 20 \times h=\frac{22}{7} \times 2 \times 2 \times 3.5$

$\Rightarrow h=\frac{22}{7} \times \frac{2 \times 2 \times 3.5}{44 \times 20}$

$\Rightarrow h=\frac{1}{20} \mathrm{~m}$

$\Rightarrow h=\frac{100}{20} \mathrm{~cm}$

$\therefore h=5 \mathrm{~cm}$

So, the height of the rainfall is 5 cm.