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 $2.5 \mathrm{~cm}$.

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Updated on: 10-Oct-2022

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