Jack is a manufacturing engineer. He has been given the job of designing an aluminum container having a square base and rectangular sides to hold screws and nails. It also must be open at the top. The container must use 200 cm² of aluminum, and it must hold as much as possible (i.e., have the greatest possible volume). What dimensions should the container have?

Sketch the sides of this container (click here to see an example). Pick a value for x and calculate the height (y).

How are x and y related? That is, how could we find y for any value of x?

Write the function definition for the volume of this container for any base length x?