Question

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

Answer 1

Side of cube = 4 cm

Volume of cube = 4 x 4 x 4 = 64cm3

The sphere touches the cube's sides. So, diameter of cube = 4 cm.

Radius = 2cm

So, volume of sphere = 4/3 pi r3 = 33.51cm3(approximately)

So, volume of the gap = V of cube - V of sphere= 64-33.51 = 30.49 cm3

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Answer 2

volume if cube is (4)^3 cm ^3
so volume if cube is 64 cm ^3

volume of sphere where radius is half of side if cube
so radius is 2 cm
volume of sphere is 4/3Πr^3
so volume if sphere is 33.2cm ^3

volume if gap in between is 64cm ^3 - 33.2cm ^3
so volume of gap in between is 30.8 cm ^3