Volume(s) of Insight

Geometry Level 5

A plane cuts a unit sphere into two 3D solid objects such that the ratio of heights of these 2 objects is the silver ratio , 1 + 2 1 + \sqrt2 .

Let P P denote the ratio of the total surface area of the smaller of these 2 objects and the surface area of the original unit sphere. Submit your answer as 100 P \lfloor 100P \rfloor .


The answer is 50.

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