A box with no top that has a volume of 1000 cubic inches is to be constructed from a 22 x 30-inch sheet of cardboard by cutting squares of equal size from each corner and folding up the flaps. If one of the dimensions has to be greater than 18 inches, what size square should be cut from each corner?

If each corner square has side length x, the box dimensions are x, 22 − 2x, and 30 − 2x. Setting the volume to 1,000 gives x(22 − 2x)(30 − 2x) = 1,000; x = 2.234 inches gives dimensions of about 2.234, 17.532, and 25.532 inches, whose product is about 1,000. The 25.532-inch dimension is greater than 18 inches, so the correct choice is 2.234 inches.

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