Q. 64.7( 7 Votes )

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

Answer :

Given: length of a side of a cube “a” =4cm

Thus, Volume of a cube = a3


Where a = side of a cube


Thus, Volume of a cube = (4)3 = 64 cm3


Now, given that A cube contains a sphere touching side of a cube,



Now, By the figure drawn above, we can say that


Diameter of a sphere = side of a cube = 4cm




Where,


r = radius of a sphere


Thus,


Volume of a gap in between cube and sphere = Volume of a cube –


Volume of a sphere


Volume of a gap in between cube and sphere = (64 – 33.52)cm3


Volume of a gap in between cube and sphere = 30.48 cm3


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