# Maxi-Mini-ma

Calculus Level 3

A trash can is to be designed. The sides of the can form a cylinder of base radius $$r$$ and height $$h$$. Also,we know that the top of the can is a hemisphere of radius $$r$$ pointing up.Based on this information,what ratio of height $$h$$ to radius $$r$$ maximizes the volume of the can for a fixed surface area $$A$$ ?

• $$h/r$$ $$=$$ $$m/n$$ where $$m$$ and $$n$$ are positive integers in their simplest form.
• input $$m+n$$.
×