Question:
A cube of side 4 cm contains a sphere touching its side. Find the volume of the gap in between.
Solution:
It is given that
Cube side = 4cm
Volume of cube $=(4 \mathrm{~cm})^{3}=64 \mathrm{~cm}^{3}$
Diameter of the sphere = Length of the side of the cube = 4cm
Therefore radius of the sphere = 2cm
Volume of the sphere $=4 / 3 \pi r^{3}=4 / 3 \times 22 / 7 \times(2)^{3}=33.52 \mathrm{~cm}^{3}$
Volume of gap = Volume of cube - Volume of sphere
$=64 \mathrm{~cm}^{3}-33.52 \mathrm{~cm}^{3}=30.48 \mathrm{~cm}^{3}$
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