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Math Help - Finding the area of this shape - almost like a triangle, but the hypotenuse is round

  1. #1
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    Finding the area of this shape - almost like a triangle, but the hypotenuse is round

    Here's my problem:

    I'm trying to figure out how to calculate the volume of this figure:



    (Please excuse the crappy drawing).

    Anyway, this is a cross section of a "ring". I usually deal with rings with rectangular cross-sections, in which case it is simple to figure out the volume:

    volume of "rectangular cross-sectioned ring":

    pi/4*(OD^2 - ID^2) * height = volume of ring

    Simple.

    But for this figure, in order to calculate the total volume, I need 3 volumes:

    VLOD - VID - 2*VR = Total volume

    Where,

    VLOD = pi/4*LOD^2*H
    VID = pi/4*ID^2*H
    VR = what I don't know how to figure out???

    The radius is actually a small portion of a much larger circle, in which I know the coordinates of the center. I'm thinking I need to find the center of gravity of this shape in order to find the area, but I've been looking and looking and looking, and I can't seem to figure this one out.

    If anyone can help, I'd greatly appreciate it. Thanks a lot!
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  2. #2
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    Quote Originally Posted by bkelly301 View Post
    Here's my problem:

    I'm trying to figure out how to calculate the volume of this figure:



    (Please excuse the crappy drawing).

    Anyway, this is a cross section of a "ring". I usually deal with rings with rectangular cross-sections, in which case it is simple to figure out the volume:

    volume of "rectangular cross-sectioned ring":

    pi/4*(OD^2 - ID^2) * height = volume of ring

    Simple.

    But for this figure, in order to calculate the total volume, I need 3 volumes:

    VLOD - VID - 2*VR = Total volume

    Where,

    VLOD = pi/4*LOD^2*H
    VID = pi/4*ID^2*H
    VR = what I don't know how to figure out???

    The radius is actually a small portion of a much larger circle, in which I know the coordinates of the center. I'm thinking I need to find the center of gravity of this shape in order to find the area, but I've been looking and looking and looking, and I can't seem to figure this one out.

    If anyone can help, I'd greatly appreciate it. Thanks a lot!

    The bulk of the volume is in the ring = OD^2 pi/4 - ID^2 pi /4)x H . The torus part must be subtracted. Take the half circle of torus area and multiply by 2pi (OD /2 -r /2) Where r is the radius of the torus. Comments?



    bjh
    Last edited by bjhopper; April 8th 2010 at 11:30 AM. Reason: correct mistake second mistake
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