Consider the following problem: a box with an open top is to be constructed from a square piece of cardboard, 3 ft 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. let x denote the length of the side of the square being cut out. let y denote the length of the base.
(a) draw several diagrams to illustrate the situation, some short boxes with large bases and some tall boxes with small bases. find the volumes of several such boxes. (do this on paper. your teacher may ask you to turn in this work.)

(b) draw a diagram illustrating the general situation. introduce notation and label the diagram with your symbols. (do this on paper. your teacher may ask you to turn in this work.)

(c) write an expression for the volume v in terms of x and y.
v =

(d) use the given information to write an equation that relates the variables. (do this on paper. your teacher may ask you to turn in this work.)

(e) use part (d) to write the volume as a function of x.
v(x) =

(f) finish solving the problem by finding the largest volume that such a box can have.
v = ft3