A rectangular beam will be cut from a cylindrical log of radius 10 inches. (a) Show that the beam of maximal cross-sectional area is a square. (b) Four rectangular planks will be cut from the four sections of the log that remain after cutting the square beam.Determine the dimensions of the planks that will have maximal cross-sectional area.   (c) Suppose that the strength of a rectangular beam is proportional to the product of its width and the square of its depth.Find the dimensions of the strongest beam that can be cut from the cylindrical log.

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