A piece of wire is cut into two pieces

MATHEMATICS · Single correct · AP · Calculus AB · Analytical Applications of Differentiation · Analytical Applications of Differentiation

Problem

A 20 cm20\text{ cm} piece of wire is cut into two pieces. One piece is bent to form a circle, and the other is bent to form a square. How much wire (in centimeters) should be used for the circle so that the combined area of the two shapes is minimized? (a) 1010 (b) 20π1+π\dfrac{20\pi}{1+\pi} (c) 20π4+π\dfrac{20\pi}{4+\pi} (d) 20π16+π\dfrac{20\pi}{16+\pi}

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