Rain water, which falls on a flat rectangular surface of length $ 6 \mathrm{~m} $ and breadth $ 4 \mathrm{~m} $ is transferred into a cylindrical vessel of internal radius $ 20 \mathrm{~cm} $. What will be the height of water in the cylindrical vessel if a rainfall of $ 1 \mathrm{~cm} $ has fallen?

Given:

Rain water, which falls on a flat rectangular surface of length \( 6 \mathrm{~m} \) and breadth \( 4 \mathrm{~m} \) is transferred into a cylindrical vessel of internal radius \( 20 \mathrm{~cm} \).

A rainfall of \( 1 \mathrm{~cm} \) has fallen.

To do:

We have to find the height of water in the cylindrical vessel.

Solution:

Length of the rectangular surface $l=6 \mathrm{~m}$

Breadth of the rectangular surface $b=4 \mathrm{~m}$

Height of the water level $h=1 \mathrm{~cm}$

$=\frac{1}{100} \mathrm{~m}$

Therefore,

Volume of the rain water $=l b h$

$=6 \times 4 \times \frac{1}{100}$

$=0.24 \mathrm{~m}^{3}$

Radius of the cylindrical vessel $r=20 \mathrm{~cm}$

Let the height of the water in the vessel be $h \mathrm{~cm}$.

This implies,

Volume of the water in the cylindrical vessel $=\pi r^{2} h$

$\pi r^{2} h=0.24 \mathrm{~m}^{3}$

$\Rightarrow \frac{22}{7} \times(20)^{2} \times h=\frac{24}{100} \times(100)^{3}$

$\Rightarrow \frac{22}{7} \times 400 \times h=24 \times 10000$

$\Rightarrow h=\frac{24 \times 10000 \times 7}{22 \times 400}$

$\Rightarrow h=190.9$

$\Rightarrow h=191 \mathrm{~cm}$

The height of water in the cylindrical vessel is $191 \mathrm{~cm}$.

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Updated on: 10-Oct-2022

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