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Homework Help: Surface area of sqrt(x^2+y^2)

  1. Nov 15, 2009 #1
    1. The problem statement, all variables and given/known data
    What's the surface area of the following 3D curve over the restricted range:

    2. Relevant equations
    **The answer is [tex]\sqrt{2}\pi[/tex]**

    The surface area equation (with partials)

    Reduces to

    So, for an as yet unknown integration range, we have

    3. The attempt at a solution
    Since the Z is restricted to [0,8] it would seem x and y should both be limited to [-8,8] but that integration range doesn't compute the the correct answer (listed above).

    What's the range of integral for both dy and dx?
  2. jcsd
  3. Nov 15, 2009 #2


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    Homework Helper

    sqrt(x^2+y^2)=8 is a circle of radius 8, isn't it? What does that tell you about the domain? But I don't see how you are going to get sqrt(2)*pi out of that.
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