Box folding

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If you were to fold all the boxes with different sizes of squares removed, you will have a set of boxes like those in the picture below.

photo of folded boxes
If you folded all 12 of the possible boxes, you would have a set like those in the picture above.  Now, which one has the largest volume? Assume that the volume only reaches as high as the edges. That is, a tall pile above the edges does not count.

Talk with the others in your group about these questions. Are all the volumes the same? Why? Why not?  How would you go about determining the volume of the different boxes?

After you have thoroughly discussed these problems, proceed to the next page.