#### Question

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

#### Solution

It is given that

Cube side = 4cm

Volume of cube =`(4cm)^3= 64cm^3`

Diameter of the sphere = Length of the side of the cube = 4cm

∴ Radius of sphere = 2cm

Volume of the sphere `=4/3πr^3 =4/3xx22/7xx(2)^3=33.52cm^3`

∴ Volume of gap = Volume of gap – Volume of sphere

=`64cm^2-33.52cm^3=30.48cm^3`

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Solution A Cube of Side 4 Cm Contains a Sphere Touching Its Side. Find the Volume of the Gap in Between. Concept: Volume of a Sphere.