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 \(m+n\).
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