Find the volume of the largest right circular cone that can be cut out of a cube whose edge is $ 9 \mathrm{~cm} $.

Given:

Edge of the cube $=9\ cm$.

To do:

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

Solution:

The largest right circular cone that can be cut out of the cube will have its diameter as the length of the edge of the cube.

Therefore,

Diameter of the cone $=9 \mathrm{~cm}$

Radius of the cone $r=\frac{9}{2} \mathrm{~cm}$

Height of the cone $h=9 \mathrm{~cm}$

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

$=\frac{1}{3} \times \frac{22}{7} \times \frac{9}{2} \times \frac{9}{2} \times 9$

$=190.93 \mathrm{~cm}^{3}$

The volume of the largest right circular cone that can be cut out of the given cube is $190.93\ cm^3$.

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Updated on: 10-Oct-2022

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