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Question

A sphere of radius 3, inscribed in a cube, is tangent to all six faces of the cube. The volume contained outside the sphere and inside the cube, in standard units, is:

A
97
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B
103
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C
109
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D
115
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Solution

The correct option is B 103
Volume of sphere is 43×πr3=π×43×33=36π=113.14
Length of cube is equal to diameter of circle, which implies a=6
Volume of cube is equal to a3=63=216
Remaining volume is 216113.14103

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