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Homework Help: Rotate a Circle Around the X/Y Axis - Cylindrical Shells

  1. Oct 24, 2012 #1
    1. The problem statement, all variables and given/known data
    Rotate the region bound by the given curve by about the x and y axis. Find the volume through the cylindrical method.
    x^2 + (y-1)^2 = 1

    2. Relevant equations
    Cylindrical method: ∫2∏xf(x)dx
    Slice Method: ∫A(x)dx

    3. The attempt at a solution
    x^2 + (y-1)^2 = 1
    x = √(2y - y^2)

    ∫2∏x(√(1-x^2)+1)dx from -1 to 1
    But this simplifies to 0... What am I doing wrong?
  2. jcsd
  3. Oct 24, 2012 #2
    Help, please?
  4. Oct 24, 2012 #3


    User Avatar
    Science Advisor

    What do you mean by rotation "about the x and y axis". I know how to rotate around a single axis but not two.
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