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Please help me with this wire problem

  1. Dec 5, 2006 #1
    1. The problem statement, all variables and given/known data

    A piece of wire 10ft long is cut into two pieces. One piece is bent into the shape of a circle and the other into the shape of a square. How should the wire be cut so that the combined area of the two figures is as small as possible

    2. Relevant equations

    3. The attempt at a solution
    radius=r and side of the square=s
    answer: r = 5/(pi+4) and s =10/(pi+4)

    I have the answer but I don't know how should I do it.... Please help
    Last edited: Dec 5, 2006
  2. jcsd
  3. Dec 5, 2006 #2
    should that be
  4. Dec 5, 2006 #3


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    Homework Helper

    Write down the equations for the area of a circle and the area of a square. The area of the circle has the parameter r (the radius) and the area of the square has the parameter s (the side of the square). Find the connection between these parameters and between the parameters a and b which represent the two cut pieces of the wire. Further on, create a sum A(a, b) = A1(a) + A2(b). Then plug in the relation between a and b (i.e. a + b = 10). Then you'll get the total area in a single variable, A(a) = ... (or A(b), doesn't matter). Differentiate with respect to that variable and set equal to zero.
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