Find the largest total surface area (including top and bottom) of a cylinder inscribed in a cone of base radius 9 and height 21.
We need to maximize the following function and :
Then we solve for in terms of obtaining:
We thus obtain the following formula for in terms of alone:
varies over the interval , where
has one stationary point at:
We conclude that the maximum possible total surface area of such a cylinder is:
I know that the surface area is S=2pir(r+h)