Arectangular tank that is 8788 ft cubed with a square base and open top is to be constructed of sheet steel of a given thickness. find the dimensions of the tank with minimum weight.

Form minimum weight, the surface area must be minimum.
Let the height be h and the lengths be x
the volume will be:
8788=hx^2
hence
h=8788/x^2
A=x^2+4xh
A=x^2+35142/x
dA/dx=2x-35152/x^2
thus
when dA/dx=0
2x-35152/x^2=0
2x=35152/x^2
hence
2x^3=35152
x^3=17576
x=26 ft
hence
h=8788/x^2=8788/26^2=13 ft
Hence the dimensions are 26 ft by 26 ft by 13 ft

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