[Math] the minimum possible exterior surface area of an open glassed-top aquarium

calculusoptimization

This is a question from Khan Academy I do not understand.

An open-topped glass aquarium with a square base is designed to hold $32$ space cubic feet of water. What is the minimum possible exterior surface area of the aquarium?

This is what I realize:

Surface area = $x^2+4xy$

Volume = $32=x^2\cdot y$

How do I use this to solve the problem?

Best Answer

Well, the fact that $y=\frac{32}{x^2}$ should allow you to rewrite the surface area in terms of $x$ only. Can you take it from there?