Consider the following problem a box with an open top is to be constructed from a square piece of cardboard 3 feet wide by cutting out a square from each of the four corners and bending up the sides Find the largest volume that such a box can have a Draw several diagrams to illustrate the situation some short boxes with large bases and some tall boxes with small base Find the volume of each configuration Does it appear that there is a maximum volume If so estimate it b Draw a diagram illustrating the general situation Let x denote the length of the side of the square being cut out Let y denote the length of the base c Write an expression for the volume V in terms of both x and y V d Use the given information to write an equation that relates the variables x and y e Use part d to write the volume as a function of only x V x f Finish solving the problem by finding the largest volume in ft that such a box can have V