A cube, of side $4\ cm$, contains a sphere touching its sides. Find the volume of the gap in between.

 Given:

A cube, of side $4\ cm$, contains a sphere touching its sides. 

To do:

We have to find the volume of the gap in between.

Solution:

Side of the cube $= 4\ cm$

This implies,

Volume of the cube $= 4^3$

$= 64\ cm^3$

Diameter of the largest sphere touching its sides $= 4\ cm$
This implies,

Radius of the sphere $=\frac{4}{2}$

$=2 \mathrm{~cm}$

Therefore,

Volume of the sphere $=\frac{4}{3} \pi r^{3}$

$=\frac{4}{3} \times \frac{22}{7} \times 2 \times 2 \times 2$

$=\frac{704}{21} \mathrm{~cm}^{3}$

The difference between their volumes $=64-\frac{704}{21}$

$=\frac{1344-704}{21}$

$=\frac{640}{21}$

$=30.48 \mathrm{~cm}^{3}$

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Updated on: 10-Oct-2022

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