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 = a^{3}

Where a = side of a cube

Thus, Volume of a cube = (4)^{3} = 64 cm^{3}

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)cm^{3}

Volume of a gap in between cube and sphere = 30.48 cm^{3}

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