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 a cube = 4 cm

As cube contains a sphere touching its sides.

So, the diameter of the sphere = 4 cm

Side of cube = Diameter of sphere

4 = Radius of sphere

Radius of sphere = `4/2` = 2

Volume of the gap = Volume of cube – Volume of sphere

= `("Side")^3 - 4/3pir^3`

= `(4)^3 - 4/3 pi xx 2^3`  ...[Since, side of cube = diameter of sphere]

= `(64 - 4/3 xx 22/7 xx 8)`

= 64 – 33.52

= 30.48 cm³

Hence, the volume of the gap between a cube and a sphere is 30.48 cm³.