Question

28. an open top box is to be formed by cutting out squares from the corners of a 50 centimeter x 30 centimeter rectangular sheet of material. The height of the box must be a whole number of centimeters. What size squares should be cut out to obtain the box with maximum volume.

a. Understanding the problem: If 6 centimeter x 6 centimeter squares are cut from from the corners, the height of the box will be 6 centimeters. In this case, what would the width and length of the box be?

b. Devising a plan: One plan for solving this problem is to systematically consider corner squares of increasing size. What is the largest square with whole-number dimensions that can be cut from the corners and still produce a box?

c. Carrying out the plan: Complete the following table and use inductive reasoning to predict the size of the corner squares needed to obtain the box of maximum volume.

Size of squares (centimeters)	Volume of box (cubic centimeters)
2x2
4x4
6x6
8x8
10x10
12x12
14x14

d. Looking back: The preceding table shows that as the size of the squares at the corners increase, the volume of the box increases for awhile and then decreases. Try a few more sizes for the squares, using whole numbers for dimensions to see if you can obtain a greater volume for the box.

Answer 1