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

Explanation

Given,side of a cube = 4cm
Side of cube = Diameter of sphere
4 = Diameter of sphere
Radius of sphere = `(4)/(2)= 2 cm `
Volume of the gap = Volume of cube - Volume of sphere
`= ("side")^(3) - (4)/(3)pir^(3)`
`= (4)^(3) - (4)/(3) pi(2)^(2)" " [because "side of cube" = "diameter of sphere"]`
` = (64 - (4)/(3) xx (22)/(7) xx 8) = 64- 33.52 = 30.48cm^(3)`
Hence, the volume of the gap in between a cube and a sphere is `30.48 cm^(3)`.