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The curved surface area of a cylinder is $1320\ cm^2$ and its base had diameter $21\ cm$. Find the height and the volume of the cylinder.
Given:
The curved surface area of a cylinder is $1320\ cm^2$ and its base had diameter $21\ cm$.
To do:
We have to find the height and the volume of the cylinder.
Solution:
Curved surface area of the cylinder $= 1320\ cm^2$
Diameter of the base $= 21\ cm$
This implies,
Radius $=\frac{21}{2} \mathrm{~cm}$
Therefore,
$2 \pi r h=1320$
$\frac{2 \times 22}{7} \times \frac{21}{2} h=1320$
$66 h=1320$
$h=\frac{1320}{66}$
$h=20$
Height $=20 \mathrm{~cm}$
Volume $=\pi r^{2} h$
$=\frac{22}{7} \times \frac{21}{2} \times \frac{21}{2} \times 20$
$=6930 \mathrm{~cm}^{3}$
The height of the cylinder is $20\ cm$ and the volume of the cylinder is $6930\ cm^3$.