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.

Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter59: Areas Of Rectangles, Parallelograms, And Trapezoids
Section: Chapter Questions
Problem 79A
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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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