MathDB
Purple Comet 2017 MS Problem 20

Source:

April 14, 2018
Purple Comet

Problem Statement

A right circular cone has a height equal to three times its base radius and has volume 1. The cone is inscribed inside a sphere as shown. The volume of the sphere is mn\frac{m}{n}, where mm and nn are relatively prime positive integers. Find m+nm + n.
https://snag.gy/92ikv3.jpg