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# Hard Geometry Question

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Polyhedron "P" is inscribed in a sphere of radius 36 (meaning that all vertices of  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 that can be inscribed in a sphere of radius 36?

Jun 29, 2020