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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