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Differentiating simple problems relating to area

  1. Jan 23, 2012 #1
    1. The problem statement, all variables and given/known data

    1. a)

    A rope 25m long is cut into two pieces. One piece is bent into the shape of a square, and the other into the shape of a circle. How should the rope be cut to maximise the total area enclosed by the pieces? And how should it be cut in order to minimise the total area enclosed by the two pieces?

    Any help would be appreciated, i'm a bit rusty on calculus, cheers
     
    Last edited: Jan 23, 2012
  2. jcsd
  3. Jan 23, 2012 #2

    SammyS

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    Hello Mjr1991. Welcome to PF !

    What have you tried?

    Where are you stuck?

    Have you read the rules of this forum? -- particularly the part regarding homework Help.
     
  4. Jan 23, 2012 #3
    The second part has now been completed! However the second part I don't understand the whole concept of splitting it into two, all I am unsure of is how to start the question, the rest should be fine, many thanks if you can push me in the right direction
     
  5. Jan 23, 2012 #4

    SammyS

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    Suppose we cut the rope in two, one piece has a length of ... let's call it L .

    What's the length of the other piece?

    If we form the piece of length L into a circle, what is the area of that circle. (You might first find it necessary to find the diameter & then the radius.)

    What's the area of the square?
     
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