## Arnold is trying to make packing boxes out of 6 foot by 6 foot pieces of cardboard from the local grocer. Help Arnold decide how much he should cut from each corner of the cardboard to make an open box for moving.Part I: Determining DimensionsArnold has been given a 6 foot by 6 foot sheet of cardboard to make an open box by cutting an equal size square from each corner, folding up the resulting flaps, and taping at the corners. Your task is to label dimensions on a sketch with the same size variable cut from each corner. *You don't have to draw one, just explain what it would look like*Part II: Analyze How does each variable expression relate to the length, width, and height of the box when folded? Part III: Extend your Findingsa. Based upon the variables you used in Part II, write a product for the volume. b. Expand the product to write a volume function. c. What domain makes sense for the volume? d. Guess and check values to find the size cut that produces a maximum volume. *Six guesses are required*

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