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Maximizing the Volume of an Open Top Box

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A square sheet of cardboard 24 inches on a side is made into a box by cutting squares of equal size from each corner of the sheet and folding the projecting flaps into an open-top box. What should be the length of the edge of any of the cutout squares to give the box maximum volume?

4 inches
4.5 inches
5.5 inches
6.5 inches
7 inches
7.5 inches
8 inches
none of these

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A square sheet of cardboard 24 inches on a side is made into a box by cutting squares of equal size from each corner of the sheet and folding the projecting flaps into an open-top ...

Solution Summary

The maximum volume of an open-top box is found. The solution is detailed and well presented. The response received a rating of "5/5" from the student who originally posted the question.

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