An homage to Archimedes

Archimedes discovered a relationship between volume of a sphere and that of a cylinder whose height was equal to the diameter of the sphere.[br][br]He also discovered a relationship among the surface areas of the cylinder and sphere and the area enclosed by a great circle of the sphere.[br][color=#ff0000][i][b][br]What questions could / would you put to your students based on this applet ?[/b][/i][/color]

Information: An homage to Archimedes