A rectangular tank with a bottom and sided but but no top is to have volume 500 cubic feet. Determine the
dimensions (length, width, height) with the smallest possible surface area.
For a minimal surface area, the top of the tank will be square.
Let's say the side of this square is x.
And let h be the height of the tank.
Then the volume is and the surface area is .
Can you combine these equations to find A as a function of x?
Afterwards its derivative needs to be zero, which will give you x.