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Thread: Find height of segment given radius and area

  1. #1
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    Find height of segment given radius and area





    I have R and I have A how do I solve for theta? From there I can figure out h.

    Or is there another formula I could use to find h if I only have the Area and the radius?
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  2. #2
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    First: This is a double posting which is against forum rules.
    Second: You did not make clear that A is the area of the shaded area in the diagram.
    Now I am prepared to be proven wrong in what follows.
    It seems to me that your question has no unique solution.
    As the circular radius increases and the angle $\displaystyle \theta$ decreases the area of the segment could remain constant.
    Therefore, you need to know a third constant.
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  3. #3
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    Found own answer

    Thanks for trying, I have been fighting with this for awhile, but I found the answer.

    You can use Newton's Method to solve for theta - sin(theta).

    BTW the diagram is from the website you sent me to so I didn't think that I would have to explain it.
    Sorry about the double post I was desperate to find the answer.
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  4. #4
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    Quote Originally Posted by lhenderson View Post




    I have R and I have A how do I solve for theta? From there I can figure out h.

    Or is there another formula I could use to find h if I only have the Area and the radius?

    Try this:
    sin theta/2=a/2R find the angle
    Then, r=R costheta/2
    h=R-r
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