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The rain water from a roof of dimensions \( 22 \mathrm{~m} \times 20 \mathrm{~m} \) drains into a cylindrical vessel having diameter of base \( 2 \mathrm{~m} \) and height \( 3.5 \mathrm{~m} \). If the rain water collected from the roof just fills the cylindrical vessel, then find the rain fall in \( \mathrm{cm} \).
Given:
The rain water from a roof of dimensions \( 22 \mathrm{~m} \times 20 \mathrm{~m} \) drains into a cylindrical vessel having diameter of base \( 2 \mathrm{~m} \) and height \( 3.5 \mathrm{~m} \).
The rain water collected from the roof just fills the cylindrical vessel.
To do:
We have to find the rain fall in \( \mathrm{cm} \).
Solution:
Length of the roof $=22 \mathrm{~m}$
Breadth of the roof $=20 \mathrm{~m}$
Let the rainfall be $a \mathrm{~cm}$.
Volume of water on the roof $=22 \times 20 \times \frac{a}{100}$
$=\frac{22 a}{5} \mathrm{~m}^{3}$
Radius of the base of the cylindrical vessel $=1 \mathrm{~m}$
Height of the cylindrical vessel $=3.5 \mathrm{~m}$
This implies,
Volume of the water in the cylindrical vessel $=(\frac{22}{7} \times 1 \times 1 \times \frac{7}{2})$
$=11 \mathrm{~m}^{3}$
Volume of the water on the roof $=$ Volume of the water in the vessel
Therefore,
$\frac{22 a}{5}=11$
$\Rightarrow a=\frac{11 \times 5}{22}$
$\Rightarrow a=2.5$
The amount of rainfall is $2.5 \mathrm{~cm}$.