a cube of side 4 cm contains a sphere touching its sides find the volume of gap in between
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Let ABCD be cube which contain sphere touching its sides.The diameter of sphere is the sides of the cube.
Now,
The volume of the gap in between cube and sphere
= volume of cube -volume of sphere
=(a)
3
−
3
4
πr
3
=(4)
3
−
3
4
×
7
22
×(
2
4
)
3
=64−
3
4
×
7
22
×8
=64−
21
704
=
21
1344−704
=
21
640
=30
=30cm
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