Hello, realintegerz!

Did you make a sketch?

A box with a square base (sides of length $\displaystyle x$) and an open top

must have a volume of 32,000 cubic centimeters.

Express the surface area as a function of the height of the box. Code:

*-------*
/| /|
/ | / |
*-------* |
| | |
| | |
h| | *
| | /
| |/ x
*-------*
x

The volume is: .$\displaystyle x^2h \:=\:32,\!000 \quad\Rightarrow\quad x^2 \:=\:\frac{32,\!000}{h} \quad\Rightarrow\quad x \:=\:\frac{80\sqrt{5}}{\sqrt{h}}$ .[1]

The surface area is comprised of:

. . a square base with area: $\displaystyle x^2$

. . four side panels, each with area: $\displaystyle xh$

The total surface area is: .$\displaystyle A \;=\;x^2 + 4xh$

Substitute [1]: .$\displaystyle A \;=\;\frac{32,\!000}{h} + 4\left(\frac{80\sqrt{5}}{\sqrt{h}}\right)h $

Therefore: .$\displaystyle \boxed{A \;=\;\frac{32,\!000}{h} + 320\sqrt{5h}}$