Since L=W, we can write the volume as ..[1]

Assuming there is a top, the surface area is ...[2]

If we want to minimize the surface area, we can solve the volume formula for H and sub into S.

From [1], ...[3]

Sub into [2]:

Differentiate, set to 0 and solve for L.

The width is the same. Plug this into [3] to find the height.

We get .

It's the same. The minimum surface area occurs when we have a cube.

That means the surface area is

Ti-83's do not do derivatives. For that get a TI-89, Voyage 200, etc.