**Question:**

The rain water from a roof of dimensions 22 m x 20 m drains into a cylindrical vessel having diameter of base 2 m and height 3.5 m. If the rain water

collected from the roof just fill the cylindrical vessel, then find the rainfall (in cm).

**Solution:**

Given, length of roof = 22 m and breadth of roof = 20 m

Let the rainfall be a cm.

$\therefore$ Volume of water on the roof $=22 \times 20 \times \frac{a}{100}=\frac{22 a}{5} \mathrm{~m}^{3}$

Also, we have radius of base of the cylindrical vessel $=1 \mathrm{~m}$ and height of the cylindrical vessel $=3.5 \mathrm{~m}$

$\therefore$ Volurne of water in the cylindrical vessel when it is just full

$=\left(\frac{22}{7} \times 1 \times 1 \times \frac{7}{2}\right)=11 \mathrm{~m}^{3}$

Now, volume of water on the roof $=$ Volume of water in the vessel

$\Rightarrow$ $\frac{22 a}{5}=11$

$\therefore$ $a=\frac{11 \times 5}{22}=2.5$ $\left[\because\right.$ volume of cylinder $=\pi \times(\text { radius })^{2} \times$ height $]$

Hence, the rainfall is $2.5 \mathrm{~cm}$