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A piece of wire 18 m long is cut into two pieces. One piece is bent into a square and the other is bent into a circle.
(a) How much wire should be used for the square in order to maximize the total area?

  • calculus -

    If x is allocated to the square, that leaves 18-x for the circle. So,
    r = (18-x)/2π

    a = π((18-x)/2π)^2 + (x/4)^2
    = (1/4π + 1/16)x^2 - 9/π x + 81/π

    now just set da/dx=0 and solve for x

  • calculus -


  • calculus -


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