Question

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

Answer 1

Side of cube $=4cm\therefore Volume=(side{)}^3=4\times 4\times 4=64c{m}^3$
Diameter of the largest sphere touching its sides $=4cm\therefore Radius=\frac{4}{2}=2cm\therefore Volume=\frac{4}{3}\pi r^3=\frac{4}{3}\times \frac{22}{7}\times 2\times 2\times 2c{m}^3=\frac{704}{21}c{m}^3$
Now difference between their volume
$=64-\frac{704}{21}c{m}^3=\frac{1344-704}{21}=\frac{640}{21}c{m}^3=30.48c{m}^3$