+0

0
130
1

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