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Math Help - Calculus II problem: Volume of the solid

  1. #1
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    Calculus II problem: Volume of the solid

    Hi, I have one problem that I am completely stuck on. It is

    x^2 + y^2 - 6x + 8 = 0

    The problem I have is setting up the actual equation. Do I make everything in terms of y, then find where y = 0 for the points?

    I tried doing this and it gave me a really funky looking graph. If anybody could point me in the right direction, that would be great!

    Thanks!
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  2. #2
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    Quote Originally Posted by kn336a View Post
    Hi, I have one problem that I am completely stuck on. It is

    x^2 + y^2 - 6x + 8 = 0

    The problem I have is setting up the actual equation. Do I make everything in terms of y, then find where y = 0 for the points?

    I tried doing this and it gave me a really funky looking graph. If anybody could point me in the right direction, that would be great!

    Thanks!
    Complete the squares:

    x^2  - 6x \bold{\color{red}+9}+ y^2 =- 8 \bold{\color{red}+9}

    (x-3)^2+y^2=1

    This equation describes a circle with the center at C(3,0) and the radius r = 1
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  3. #3
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    If I am trying to integrate that, I just have to put that in terms of dy or dx right?
    Last edited by kn336a; July 6th 2009 at 12:52 AM.
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  4. #4
    MHF Contributor matheagle's Avatar
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    are you trying to find volume or area?
    as pointed out this is a circle in just two dimensions.
    are you revolving it about a line or is there some constraints on the z-axis?
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  5. #5
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    Sorry, here is my entire question.

    Find the volume of the solid obtained by revolving the region bounded by the curve x^2 + y^2 - 6x + 8 = 0

    im pretty stuck right now.
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  6. #6
    MHF Contributor matheagle's Avatar
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    Quote Originally Posted by kn336a View Post
    Sorry, here is my entire question.

    Find the volume of the solid obtained by revolving the region bounded by the curve x^2 + y^2 - 6x + 8 = 0

    im pretty stuck right now.

    still incomplete
    revolving about what?
    I'm guess either x=2, x=4, maybe the y-axis...

    You need to draw this for several reasons.
    First to understand the question and why it's incomplete
    and later to figure out how to integrate it (shells vs. washers, dx or dy...)
    NITE, it's 3:45 AM here
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  7. #7
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    lol, so sorry. it's about the y-axis. im getting a little tired
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