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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