A rectangular tank with a square base, an open top, and a volume of 864 ft^3 is to be constructed of the sheet steel. Find the dimensions of the tank that minimize the surface area

Answer 1

s^2 h = 864
A = s^2 + 4 s h

4 s (864/s^2) + s^2 = A
so
A = 3456 /s + s^2
now I will trust that you really mean calculus
dA/ds = -3456/s^2 + 2 s = 0 for max or min
or
3456 = 2 s^3
s^3 = 1728
s = 12
12 * 12 * 6