The open tray shown in the illustration is to be manufactured from a 18-by-19-inch rectangular sheet of metal by cutting squares from each corner and folding up the sides. if the volume of the tray is to be 440 cubic inches and x is to be an integer, what size squares should be cut from each corner?

You should cut out squares that are 4 inches by 4 inches.

One of the ways to do this problem is write and graph an equation. We can write an equation for the volume of this shape and then use a graphing calculator to graph it. If we look where the graph crosses 440, we will have our solution.

The volume needs to be 440. If we let x equal the side of the square that is cut out, we have the following dimensions.

Length = 19 - 2x
Width = 18 - 2x
Height = x

Volume = LWH

So our equation could be: y = (19 - 2x)(18 - 2x)x

If you graph that equation, it will intersect at the point (4, 440). Therefore, our square could be 4 by 4 inches.

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