A 10-inch square piece of metal is to be used to make an open-top box by cutting equal-sized squares from each corner and folding up the sides. The length, width, and height of the box are each to be less than 6 inches. Round your answers to the following questions to three decimal places.
(a) If the box is to have a volume of 50 cubic inches, what size squares should be cut from each corner?
(b) What size squares should be cut to produce a box with the largest possible volume?
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