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Hello, I am having problems with this geometry problem. Please help! Thanks.

Polyhedron \(P\) is inscribed in a sphere of radius \(36\) (meaning that all vertices of \(P\) lie on the sphere surface). What is the least upper bound on the ratio\(\frac{\text{volume of }P}{\text{surface area of }P}~?\)

In other words, what is the smallest real number \(t\) such that

\(\frac{\text{volume of }P}{\text{surface area of }P} \le t\)

must be true for all polyhedra \(P\) that can be inscribed in a sphere of radius 36?

 Mar 11, 2019
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The smallest such real number is 24.

 Dec 1, 2019

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