Question

A cube of side $4$ cm contains a sphere touching its sides. Find the volume (cm${}^3$) of the gap in between. (Round your answer to nearest whole number)

Answer 1

Let ABCD be cube which contain sphere touching its sides.The diameter of sphere is the sides of the cube.

Now,

The volume of the gap in between cube and sphere

= volume of cube -volume of sphere

$={\left(a\right)}^3-\frac{4}{3}\pi r^3={\left(4\right)}^3-\frac{4}{3}\times \frac{22}{7}\times {\left(\frac{4}{2}\right)}^3=64-\frac{4}{3}\times \frac{22}{7}\times 8=64-\frac{704}{21}=\frac{1344-704}{21}=\frac{640}{21}=30=30{cm}^3$