Let x be the length of the cut. Then the sides of the box formed are 10-2x by 10-2x by x. (x will be the "height" or depth of the open box; there are two corners for each side so the length of the side is 10-2x)

The volume of the box is l x w x h or:

V=(10-2x)(10-2x)x

You indicate that you are to proceed by guess and check: you should form a table of possible cuts and the associated volume:

Expanding the product we get `V=4x^3-40x^2+100x`

Note that there are some natural restraints on x (the...

(The entire section contains 230 words.)

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