A rectangular 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