You cut square corners off a peice of cardboard with dimensions 16 inch by 20 inch. You then fold the cardboard to create a box with no lid. To the nearest inch what dimensions will give you the greatest volume?

For every square inch you take off of the 4 corners, both side dimensions will go down by 2 while the height goes up by 1.

So,

1in^2 : 16-2 by 20-2 by 1 = 14 * 18 * 1 = 252

2in^2 : 16-4 by 20-4 by 2 = 12 * 16 * 2 = 384

3in^2 : 16-6 by 20-6 by 3 = 10 * 14 * 3 = 420

4in^2 : 16-8 by 20-8 by 4 = 8 * 12 * 4 = 384

Since 3in^2 gave you the greatest volume, the dimensions were 10 * 14 * 3.

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