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If a sphere of radius 3 is inscribed in ...

If a sphere of radius 3 is inscribed in a cube such that it is tangent to all six faces of the cube, the volume contained outside the sphere and inside the cube is

A

97

B

103

C

109

D

115

Text Solution

Verified by Experts

The correct Answer is:
B
The cube is `6xx6xx6`, so its volume is 216. The sphere has radius 3, so
Volume of sphere `=(4)/(3)pi r^(3)`
`=(4)/(3)pi(3^(3))`
`= 36 pi`
The difference is `216 - 36pi~~103`.
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