Creation of this applet was inspired by a [url=https://twitter.com/LukeSelfwalker/status/932364944598863872]tweet[/url] from [url=https://twitter.com/LukeSelfwalker]Luke Walsh[/url]. [br][br]In the applet below, the sphere is inscribed inside the right circular cone. [br]The radius of the sphere = [math]\pi[/math]. [br][br][b]Questions to consider:[/b] [br][br]Is there a height of such a cone that will minimize the cone's volume? [br][br]What percentage of the volume of the cone is the volume of the largest possible sphere? [br][br]How can we use calculus to prove this formally? [br]