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Minimising the materials used for a circular gutter.

  1. Aug 20, 2010 #1
    1. The problem statement, all variables and given/known data
    A plastic gutter is designed to catch water at the edge of a roof.

    Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter? In this case, a circle.

    2. Relevant equations
    None, asside from Geometry.

    3. The attempt at a solution
    From my thinking, we need to minimise the perimeter of the circle (minus the gap for water to be let in - the arc length) and maximise the area. My problem is, how do I go about it? We would need to find the circumference minus the arc length and differentiate that to find the minimum perimeter and then set it against the maximised area of the circle? I'm rather confused. :|
  2. jcsd
  3. Aug 20, 2010 #2
    There really isn't enough given information to fully solve the problem, the way I see it.
  4. Aug 21, 2010 #3
    Well, here's the problem in its entirety:

    We weren't given anything else to work with.
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