My Math Forum Area of a segment of a circle from % of height.

 Algebra Pre-Algebra and Basic Algebra Math Forum

 October 24th, 2011, 08:59 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, 09:33 AM #2 Global Moderator   Joined: Dec 2006 Posts: 21,028 Thanks: 2259 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, 01:36 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, 01:15 PM #4 Global Moderator   Joined: Dec 2006 Posts: 21,028 Thanks: 2259 Can you follow this article?
 October 26th, 2011, 11:00 PM #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, 03:58 AM #6 Global Moderator   Joined: Dec 2006 Posts: 21,028 Thanks: 2259 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, 09:34 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.

 Tags area, circle, height, segment

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post Pivskid Algebra 11 July 3rd, 2013 08:25 AM wuzhe Algebra 3 October 27th, 2012 06:04 PM Tutu Algebra 3 May 8th, 2012 07:14 AM kthr33 Algebra 2 January 8th, 2009 05:13 AM sterling748 Algebra 4 November 17th, 2008 09:28 AM

 Contact - Home - Forums - Cryptocurrency Forum - Top