Arectangular tank that is 5324 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.

Side of 22 and height of 11

Step-by-step explanation:

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