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Surface Area problem

  1. Jan 31, 2007 #1
    1. The problem statement, all variables and given/known data
    I am wondering if someone could help me with the following? I am supposed to find the area of the finite part of the paraboloid y = x^2+z^2 that's cut off by the plane y = 25. Now, wouldn't this be the same as the paraboloid z = x^2+y^2 that's cut off by the plane z = 25?

    So, if that's right, then the surface area is ∫∫√((dz/dx)^2+(dz/dy)^2+1).
    This seems easier to do in polar coordinates, so we basically have the following:

    ∫∫(1+4r^2)? And, r would be from 0 to 5, and 0≤θ≤2*pi?

    Am I doing something wrong here? Or, how do I "project" the surface unto the x-z plane? Thanks!!!
  2. jcsd
  3. Jan 31, 2007 #2


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    Why do you think you are doing something wrong? Well done.
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