Sphere Inscribed Inside a Right Circular Cone

Creation of this applet was inspired by a tweet from Luke Walsh. In the applet below, the sphere is inscribed inside the right circular cone. The radius of the sphere = . Questions to consider: Is there a height of such a cone that will minimize the cone's volume? What percentage of the volume of the cone is the volume of the largest possible sphere? How can we use calculus to prove this formally?

Quick (Silent) Demo