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 $6930\ cm^3$.

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Updated on: 10-Oct-2022

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