Posted by **deel** on Saturday, August 11, 2012 at 11:10pm.

A right circular cylinder of radius r and height h is inscribed in a right circular cone of radius R and height H, as shown on the right figure. Find the value of r (in terms of R and H) that maximizes the total surface area of the cylinder (including top and bottom). Comment on the influence of the relationship between R and 2H to the max/min of total surface area.