MathDB
2000 HMMT RMT Geometry # 8

Source:

March 3, 2024
geometry

Problem Statement

A sphere is inscribed inside a pyramid with a square as a base whose height is 152\frac{\sqrt{15}}{2} times the length of one edge of the base. A cube is inscribed inside the sphere. What is the ratio of the volume of the pyramid to the volume of the cube?