Question

Question 6
A cube of side 4 cm contains a sphere touching its sides. Find the volume of the gap in between.

Answer 1

Given, side of the cube = 4 cm
Side of cube = Diameter of the sphere
Diamter = 4 cm
$\therefore$ Radius of the sphere $=\frac{4}{2}=2cm$
Volume of the gap = Volume of cube - Volume of sphere
$=(Side{)}^3-\frac{4}{3}\pi r^3$
$=(4{)}^3-\frac{4}{3}\pi (2{)}^3$ [$\because$ side of cube = diameter of sphere]
$=(64-\frac{4}{3}\times \frac{22}{7}\times 8)=64-33.52=30.48c{m}^3$