Question

suppose that we wish to create an open-top box with a square base which uses different a material for the base vs. the sides. the material for the base will cost and the material for the sides will cost . if the box must have a volume of , what is the minimum material cost for the box?

Answer 1

Polyhedron is inscribed in a sphere of radius (meaning that all vertices of lie on the sphere surface). What is the least upper bound on the ratio In other words, what is the smallest real number such that must be true for all polyhedra that can be inscribed in a sphere of radius ?