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October 24th, 2011, 09:59 AM  #1 
Newbie Joined: Oct 2011 Posts: 4 Thanks: 0  Area of a segment of a circle from % of height.
Hi, Can anyone help me to calculate the area of a segment of a circle when it is expressed as a percentage of the height? For example if a circle is 750mm in diameter and the segment consists of the bottom 5% of the total height (37.5mm) what would the area of this segment be? Help for a first time user would be much appreciated. Regards, John. 
October 24th, 2011, 10:33 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,156 Thanks: 1422 
You are using "total height" to refer to the circle's diameter. If you are given the diameter and the percentage, you can calculate the height of the segment, and then use trigonometry to find the angle subtended by the segment. After that, finding the area is easy.

October 25th, 2011, 02:36 AM  #3 
Newbie Joined: Oct 2011 Posts: 4 Thanks: 0  Re: Area of a segment of a circle from % of height.
Skipjack, Thanks for that, but it's finding the angle that I'm having the issue with........ Any further advice ??? 
October 25th, 2011, 02:15 PM  #4 
Global Moderator Joined: Dec 2006 Posts: 18,156 Thanks: 1422 
Can you follow this article?

October 27th, 2011, 12:00 AM  #5 
Newbie Joined: Oct 2011 Posts: 4 Thanks: 0  Re: Area of a segment of a circle from % of height.
I'm afraid not. I can work out the chord length but then I'm lost when it comes to working out the angle. Any chance you could show me an example with the working and I could probably take it from there? 
October 27th, 2011, 04:58 AM  #6 
Global Moderator Joined: Dec 2006 Posts: 18,156 Thanks: 1422 
You don't need the chord length. Using the article's notation, R = 750mm/2 = 375mm, h = 37.5mm, and d = R  h = 337.5mm, so ? = 2arccos(337.5/375) = 2arccos(0.9) = 0.9020536 approximately (in radians), and A = (375²/2)(0.9020536  sin(0.9020536))mm² = 8258.33mm² approximately. 
October 27th, 2011, 10:34 AM  #7 
Newbie Joined: Oct 2011 Posts: 4 Thanks: 0  Re: Area of a segment of a circle from % of height.
skipjack, Thanks a lot for that, I really appreciate it. It's been a while since I had anything to do with trigonometry and there's no way I would have got there on my own. Much appreciated..... John. 

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area, circle, height, segment 
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