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Math Help - how to find the volume of a figure with this cross section

  1. #1
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    how to find the volume of a figure with this cross section

    Hello, I need to figure out how to find the volume of this shape with a cross-sectional area that looks like this. This shape is rotated around a central axis to make a "ring".:




    It is basically a triangle, but the hypotenuse is a small portion of a much larger circle instead of a straight line.

    In order to find the volume of this "ring", I would first need to find the area of this shape, A. I would also need to find the center of gravity x-coordinate of the shape. Cgx I'll call it.

    Once I have that information, I'd be able to find the volume of this ring. The volume would be:

    Vr = 2*pi*A*(D+Cgx), where D is the distance from the center axis to the right leg of the shape.

    I don't know how to find A or Cgx though...Can anyone help me with this please? Thanks a lot!
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  2. #2
    Junior Member eddie2042's Avatar
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    answer

    use the diagram below to help you determine the area and find the centroid.

    Cheers!

    how to find the volume of a figure with this cross section-1.jpg
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  3. #3
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    Thanks a lot! I appreciate it.
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  4. #4
    Junior Member eddie2042's Avatar
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    Quote Originally Posted by bkelly301 View Post
    Thanks a lot! I appreciate it.

    So did u get the right answer?
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  5. #5
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    I'm not sure yet. I will be back at work on monday, and I will test it out first thing in the morning. To see how the problem applies to my job, I posted this same question in the geometry section, but it has more detail. I didn't get any replies there though. I'll keep you updated on Monday. Thanks again!
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  6. #6
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    Yes, that worked! Thank you very much!
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