If you fit the largest possible right circular cone inside a sphere, what fraction of the volume of the sphere is occupied by the cone? {{CMD_94}} {{ENV_95}} {{CMD_96}} {{CMD_97}} Let {{MATH_98}} be the radius of the sphere, and let {{MATH_99}} and {{MATH_100}} be the base radius and height of the cone inside the sphere. Our goal is to maximize the volume of the cone: {{MATH_101}}. The largest {{MATH_102}} could be is {{MATH_103}} and the largest {{MATH_104}} could be is {{MATH_105}}.