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Math Help - 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 \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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