Find the volume of the largest right circular cone that can be fitted in a cube whose edge is $14\ cm$.

 Given:

The edge of a cube is $14\ cm$.

To do:

We have to find the volume of the largest right circular cone that can be fitted in the cube.

Solution:

Side of the cube $= 14\ cm$

Radius of the largest cone that can be fitted in the cube $(r)=\frac{\text { Side }}{2}$

$=\frac{14}{2} \mathrm{~cm}$

$=7 \mathrm{~cm}$

Height of the cone $(h)=14 \mathrm{~cm}$

Therefore,

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

$=\frac{1}{3} \times \frac{22}{7} \times 7 \times 7 \times 14$

$=\frac{2156}{3}$

$=718.67 \mathrm{~cm}^{3}$

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Updated on: 10-Oct-2022

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