# Maximum Volume of an Open-Top Box

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

https://brainmass.com/math/geometry-and-topology/maximum-volume-of-an-open-top-box-139474

#### Solution Preview

Denote by x the length of the edge of any of the cutout squares. Then we can form the volume V(x) of the corresponding open-top box.

Note that the base is a square with equal length 24-2x. The height is x. ...

#### 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.