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Volume of a circle

  1. Jun 18, 2009 #1
    http://users.on.net/~rohanlal/circle2.jpg [Broken]
    this is part of the solution to finding the volume of a circle with double integrals.
    I just want to know where the r from rdrd0 came from and also
    why the limits on the d0 integral are 2pi and 0.
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Jun 18, 2009 #2

    Hootenanny

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    I assume you mean this is part of a question to find the volume of the cylinder created by extruding a circle along the z-axis.

    To answer your first question, the integral has be transformed from Cartesian to polar coordinates. Rather than specifying the position of a point in terms of it's (x,y) coordinates, polar coordinates uses (r,Θ), where r is the distance from the origin to the point and Θ is the angle between the radius and the positive x semi-axis. For more information and answers to your subsequent questions see http://mathworld.wolfram.com/PolarCoordinates.html" [Broken].
     
    Last edited by a moderator: May 4, 2017
  4. Jun 18, 2009 #3
    What makes you think its a cylinder?
    This is the full solution:
    http://users.on.net/~rohanlal/circ3.jpg [Broken]
     
    Last edited by a moderator: May 4, 2017
  5. Jun 18, 2009 #4

    HallsofIvy

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    This is the volume of a sphere, not a circle- circles don't have "volume"!

    And you should have learned that the "differential of area in polar coordinates" is [itex]r dr d\theta[/itex] when you learned about integrating in polar coordinates. There are a number of different ways of showing that. I recommend you check your calculus book for the one you were expected to learn.
     
    Last edited by a moderator: May 4, 2017
  6. Jun 18, 2009 #5
    and why is the limit 2pi to 0?
     
  7. Jun 19, 2009 #6

    Hootenanny

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