Consider the following problem: A box with an open top isto be constructed from a square piece of cardboard, 3 ftwide, by cutting out a square from each of the four cornersand bending up the sides. Find the largest volume that sucha box can have.(a) Draw several diagrams to illustrate the situation, someshort boxes with large bases and some tall boxes withsmall bases. Find the volumes of several such boxes.Does it appear that there is a maximum volume? If so,estimate it.

Question

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.
(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.
Does it appear that there is a maximum volume? If so,
estimate it.

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