A piece of wire 60 cm long is cut into two pieces

MATHEMATICS · Single correct · A Level · Mathematics · Differentiation · Differentiation

Problem

A piece of wire 60 cm long is cut into two pieces. One piece is bent to form a square, and the other piece is bent to form a circle. Which of the following gives the length of wire, in centimeters, that should be used for the square so that the total area enclosed by both shapes is maximized? (a) 480π+8\dfrac{480}{\pi+8} (b) 240π+4\dfrac{240}{\pi+4} (c) 960π+16\dfrac{960}{\pi+16} (d) 60π+4\dfrac{60}{\pi+4}

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