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