1. The main condition contains the value which becomes extreme that means minimal or maximal. Withe your problem it is the surface of the cylindrical can:
. That is a function with 2 variables.
2. You know additional conditions: The volume of the can must be a constant and the height of the can doesn't exceed a given value:
. Solve for h and plug in this term into the equation of 1..
. You'll get the characteristical function:
4. The surface A is extreme if the first derivative of A equals zero:
. Plug in the value for V = 500 and you'll get:
. Now plug in this value into the equation to calculate h:
. That means the diameter and the height of the can are equal, the can has a quadratical shape. The height is in the bound of the given range.