Calc question: A piece of wire 16in long is to be cut into two pieces....

Question

A piece of wire 16in long is to be cut into two pieces. One piece is bent to form a square and the other a circle. Where should the wire be cut in order for the sum of the areas of the circle and square to be Minimized? ( You may also use the whole wire to form either a square or circle.)

Answer 1

Suppose you cut into 2 pieces length x, 16-x

Square is formed from 16-x, so side of square is (16-x)/4, area (16-x)^2/16

Circle is formed from x, circumference = x, radius = x/2π, area = π (x/2π)^2 = x^2 / 4π

Total area A = (16-x)^2/16 + x^2/4π

Solve dA/dx = 0