A cylinder is inscribed in a right circular cone of height 6.5 and radius (at the base) equal to 6. What are the dimensions of such a cylinder which has maximum volume?

Answer 1

there are lots of solutions to this online. A good one is at

http://answers.yahoo.com/question/index?qid=20080427160136AACsLX6

where they show that the largest such cylinder has volume 4/9 the volume of the cone. That is, when the cylinder has 1/3 the height of the cone.

Answer 2

796