A rectangular beam is cut from a cylindrical log of radius 25 cm. A cross-section of the log is shown below. The strength, S, of a beam of width w and height h is proportional to wh2.
(a) Express the strength of the beam as a function of w only. Use k as the proportionality constant.
S (w) =
(b) Find the exact width and height of the beam of maximum strength.
Width =
Height =
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