The circumference of the base of a cylindrical vessel is $ 132 \mathrm{~cm} $ and its height is $ 25 \mathrm{~cm} $. How many litres of water can it hold? $ \left(1000 \mathrm{~cm}^{3}=1 l\right) $.

Given:

The circumference of the base of a cylindrical vessel is \( 132 \mathrm{~cm} \) and its height is \( 25 \mathrm{~cm} \).

To do:

We have to find the volume of water it can hold.

Solution:

Circumference of the base of the cylindrical vessel $= 132\ cm$

This implies,

$2\pi r = 132$

$2 \times \frac{22}{7} \times r =132$

$r=\frac{132 \times 7}{44}$

$r=21 \mathrm{~cm}$

Therefore,

Volume of the cylinder $=\pi r^{2} h$

$=\frac{22}{7} \times (21)^2 \times 25$

$=34650 \mathrm{~cm}^{3}$

We know that,

$1000 \mathrm{~cm}^{3}=1 \mathrm{~L}$

$1 \mathrm{~cm}^{3}=\frac{1}{1000} \mathrm{~L}$

This implies,

Volume $=34650 \mathrm{~cm}^{3}$

$=\frac{34650}{1000} \mathrm{~L}$

$=34.65 \mathrm{~L}$

The cylindrical vessel can hold $34.65\ L$.

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