Trying to design an aluminum can containing a volume of 2,000 cubic centimeters.

Find the dimensions of the can that will minimize the amount of aluminum used.

The three formulas I'm working with will obviously

Volume: π r^{2 }h=2000

Vertical surface area: 2π r h

Lid and base surface area: π r^{2 }(x2)

I understand that basically what I'm trying to do is isolate one variable (for example make h=2000/π r^{2}) so that I can now substitute that equation in for the variable h in another formula.

That will result in a quadratic equation, from which I will find the derivative, find max and min, and figure out the volume at the minimum. Am I missing something? I keep attempting this, but I keep getting stuck after I substitute 2000/πr^2 for h because I don't have a quadratic equation to work with.