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# Help with Geo

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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 $$36$$?

Dec 30, 2020