Find the volume of a right circular cone with height $21\ cm$ and slant height $28\ cm$.

 Given:

The height of a right circular cone is $21\ cm$ and its slant height is $28\ cm$.

To do:

We have to find the volume of the right circular cone.

Solution:

Height of the cone $(h)=21 \mathrm{~cm}$

Slant height of the cone $(l)=28 \mathrm{~cm}$

Therefore,

Radius of the cone $(r)=\sqrt{l^{2}-h^{2}}$

$=\sqrt{(28)^{2}-(21)^{2}}$

$=\sqrt{784-441}$

$=\sqrt{343}$

Volume of the cone $=\frac{1}{3} \pi r^{2} h$

$=\frac{1}{3} \times \frac{22}{7}(\sqrt{343})^{2} \times 21$

$=\frac{1}{3} \times \frac{22}{7} \times 21 \times 343$

$=7546 \mathrm{~cm}^{3}$ 

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Updated on: 10-Oct-2022

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