The largest cone is curved out from a solid cube of side $ 21 \mathrm{~cm} $. Find the volume of the remaining solid.

Given:

The largest cone is curved out from a solid cube of side \( 21 \mathrm{~cm} \).

To do:

We have to find the volume of the remaining solid.

Solution:

Length of the side of the solid cube $a= 21\ cm$

This implies,

Volume of the cube $= a^3$

$= (21)^3$

$= 9261\ cm^3$

Diameter of the base of the cone $= 21\ cm$

This implies,

Radius of the cone $r =\frac{21}{2}$

Height of the cone $h = 21\ cm$

Therefore,

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

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

$=\frac{4851}{2}$

$=2425.5 \mathrm{~cm}^{3}$

Volume of the remaining solid $=$ Volume of the cube $-$ Volume of the cone

$=9261-2425.5$

$=6835.5 \mathrm{~cm}^{3}$

The volume of the remaining solid is $6835.5\ cm^3$.

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Updated on: 10-Oct-2022

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