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Math

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You have a wire that is 35 cm long. You wish to cut it into two pieces. One piece will be bent into the shape of a square. The other piece will be bent into the shape of a circle. Let A represent the total area of the square and the circle. What is the circumference of the circle when A is a minimum?

  • Math -

    square
    side = s, area = s^2
    circle
    circumference = c, area = pi d^2/4 = c^2/(4pi)

    4s + c = 35 so c = (35-4s)
    a = s^2 + c^2/(4pi)
    a = s^2 + (35-4s)^2/(4pi)
    a = s^2 + (1225-280s+16s^2)/12.56
    a = 2.27s^2 - 22.3 s + 97.5

    that is a parabola, find the vertex or use calculus (I used calculus)
    0 = 4.54 s -22.3
    s = 4.91
    c = 35-4*4.91 = 15.3

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