what does this have to do with exponential functions? this is an optimization problem, and no exponential functions are involved

Let

be the side length of the base.

Let

be the height

Then we have the volume given by:

this is our constraint, and from it we can deduce that

now we want to construct a (i'm assuming closed top) box with the above volume and minimal surface area.

the surface area of this box is given by:

since

, we have:

this is the function we want to minimize, just find its minimum value