Hope you can see the picture and understand the drawings.
It can seem complex at first but you just have to think it through.
I use pythagoras' theorem to find the diagonal of the base square and then use that information along with the height with the aid of that ever so handy pythagoras' theorem to find the length of the slope.
Let s be the side of the square base and h be the height of the tank. Since the tank volume is restricted to 5324 ft cubed we have the following equation:
As the thickness is already defined, we can minimize the weight by minimizing the surface area of the tank
Base area with open top
Side area 4sh
Total surface area
We can substitute
To find the minimum of this function, we can take the first derivative, and set it to 0