Minimum weight => minimum area
Area = area of the base + area of the four sides
Length of the side of the square base: x
area of the base = x^2
area of the other four sides = 4 * x * height
Now you have to put height in therms of x using the volume formula:
Volume = area of the base * height => height = Volume / area of the base
height = 6912 / x^2 => area of the four sides = 4*x*6912 / x^2 = 27648 /x
Total area = x^2 + 27648/x
That is the function that you have to optimize (find the derivative and equal it to zero).
I think this is enough information to you develop the proble,
