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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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