Question

The rain water from a roof of dimensions 22 m, 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.

Answer 1

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 = $20\times 22\times \frac{a}{100}=\frac{22a}{5}{m}^3$
Also, we have radius of base of the cylindrical vessel = 1 m
And height of the cylindrical vessel = 3.5 cm
$\therefore$ Volume of water in the cylindrical vessel when it is just full
$[Volumeofcylinder=\pi \times (radius{)}^2\times height]$
$=(\frac{22}{7}\times 1\times 1\times \frac{7}{2})=11m^3$
Now, volume of water on the roof = Volume of water in the vessel
$\Rightarrow \frac{22a}{5}=11$
$\therefore a=\frac{11\times 5}{22}=2.5$
Hence , the rainfall is 2.5 cm.