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Math Help - Volume of outside of flat topped cone

  1. #1
    als
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    Volume of outside of flat topped cone

    I have an object that looks like this.



    It started as a solid cylinder, but parts have been cut off, and I need to calculate the volume of what was cut off. I've calculated the volume of cylinder that was cut out in the middle, and the cylinder cut off from the outside (the left 2 inches of the image), but I'm having trouble calculating the volume of the outside cut off on the right 2 inches.

    I started off figuring that I can somehow use the triangle shape (height .5, base 2) to my advantage, but I'm not sure what to do. I've considered using some form of integral calculus, like shell method or something, but I have no idea where to start.

    Any help is appreciated, thanks.

    P.S. May have posted in wrong area of forum. May want to move to Analysis, Topology, and Differential Geometry.
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  2. #2
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    Quote Originally Posted by als View Post
    ...

    It started as a solid cylinder, but parts have been cut off, and I need to calculate the volume of what was cut off. I've calculated the volume of cylinder that was cut out in the middle, and the cylinder cut off from the outside (the left 2 inches of the image), but I'm having trouble calculating the volume of the outside cut off on the right 2 inches.

    I started off figuring that I can somehow use the triangle shape (height .5, base 2) to my advantage, but I'm not sure what to do. I've considered using some form of integral calculus, like shell method or something, but I have no idea where to start.

    ...
    Your object consists of a cylinder and a frustum of a cone with a common cylinder taken out.

    Have a look here: Conical Frustum -- from Wolfram MathWorld
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  3. #3
    als
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    Thanks! In addition, it's useful to now know some new terminology - Frustum.
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