Results 1 to 7 of 7

Thread: Calculating segment height with only the area of segment and radius of circle

  1. #1
    Newbie
    Joined
    Oct 2017
    From
    england
    Posts
    4

    Calculating segment height with only the area of segment and radius of circle

    I have been struggling to find a method to do this (that I can understand).
    I have a bar with a diameter of 65mm.
    It has to have a segment with a 10% cross sectional area of the full circle.
    This is the data no angles or arc lengths etc.
    I need to calculate the segment width or height.
    Thanks in advance if any one can point me in the right direction.
    I have drawn it in cad and have a rough idea it is approximately 10mm.
    This was done by trial and error.
    please see my jpeg image sketch for clarity.
    Thankyou
    Matt
    Attached Thumbnails Attached Thumbnails Calculating segment height with only the area of segment and radius of circle-segment-height.jpg  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    5,919
    Thanks
    2491

    Re: Calculating segment height with only the area of segment and radius of circle

    From this page

    and your specifics we have

    $R=65$

    $h$ is the value you are after

    $A=R^2 \cos^{-1}\left(\dfrac{R-h}{R}\right) - (R-h)\sqrt{2 R h - h^2}$

    and you want

    $\dfrac{A}{\pi R^2} = 0.1$

    Solving this numerically (cause it's not going to be solved any other way) Mathematica gets

    $h=20.342$
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2017
    From
    england
    Posts
    4

    Re: Calculating segment height with only the area of segment and radius of circle

    Thankyou very much.
    I have tried plugging the numbers in to the formula but it does not work out for me. (by the way the radius was 32.5)
    My 10% area is approx 331 but when I put in R=32.5 and h=10.216 into the above formula I get a ridiculous answer.
    Matt
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    5,919
    Thanks
    2491

    Re: Calculating segment height with only the area of segment and radius of circle

    Quote Originally Posted by matty1971 View Post
    Thankyou very much.
    I have tried plugging the numbers in to the formula but it does not work out for me. (by the way the radius was 32.5)
    My 10% area is approx 331 but when I put in R=32.5 and h=10.216 into the above formula I get a ridiculous answer.
    Matt
    looks ok to me

    Calculating segment height with only the area of segment and radius of circle-clipboard01.jpg
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Oct 2017
    From
    england
    Posts
    4

    Re: Calculating segment height with only the area of segment and radius of circle

    I forgot to change to radians.
    It works on paper now.
    I do not have this software.
    Thankyou for your help.
    Matt
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Oct 2017
    From
    england
    Posts
    4

    Re: Calculating segment height with only the area of segment and radius of circle

    Unfortunately my maths ability is not great and I cannot transpose the formula to solve for h.( I already know the area which is 331)
    Mat
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor
    Joined
    Nov 2013
    From
    California
    Posts
    5,919
    Thanks
    2491

    Re: Calculating segment height with only the area of segment and radius of circle

    Quote Originally Posted by matty1971 View Post
    Unfortunately my maths ability is not great and I cannot transpose the formula to solve for h.( I already know the area which is 331)
    Mat
    that's right you can't

    it's not going to have a clean closed form solution

    it will have to be solved numerically each time you want to do this.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Calculating the height of a circle segment
    Posted in the Geometry Forum
    Replies: 3
    Last Post: Jul 1st 2016, 02:11 PM
  2. Replies: 2
    Last Post: Nov 15th 2015, 12:33 PM
  3. area of segment of a circle
    Posted in the Geometry Forum
    Replies: 1
    Last Post: Nov 4th 2010, 12:57 AM
  4. Find height of segment given radius and area
    Posted in the Geometry Forum
    Replies: 3
    Last Post: Apr 12th 2009, 07:48 AM
  5. Find height of segment given radius and area
    Posted in the Geometry Forum
    Replies: 4
    Last Post: Apr 1st 2009, 03:25 PM

/mathhelpforum @mathhelpforum