My Math Forum Circle segment area

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 June 28th, 2013, 03:25 AM #1 Newbie   Joined: Jun 2013 Posts: 6 Thanks: 0 Circle segment area Hi there Problem: Of a circle segment is known: Area and radius. Wanted: Height from the circle circumphere ot the chord. I know the formula for the circle segment it is to found everywhere. But how do I resolve it to return the height ? NOTE: the angle is NOT known.
 June 28th, 2013, 04:08 AM #2 Math Team     Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 234 Re: Circle segment area You can find the angle in radians using $A \= \ \frac{1}{2}r^2 \theta$ Then use that angle to find the height of the isosceles triangle Then subtract that from the radius.
 June 30th, 2013, 12:03 AM #3 Newbie   Joined: Jun 2013 Posts: 6 Thanks: 0 Re: Circle segment area It is a circle segment not sector. If I: A/0.5*r^2= (radians-Sin(radians) How do I get the radians out ?
June 30th, 2013, 03:00 AM   #4
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Re: Circle segment area

Quote:
 Originally Posted by Pivskid It is a circle segment not sector. If I: A/0.5*r^2= (radians-Sin(radians) How do I get the radians out ?
If you know A and you know r then $\ \theta \$ is in radians automatically.

 June 30th, 2013, 11:35 PM #5 Newbie   Joined: Jun 2013 Posts: 6 Thanks: 0 Re: Circle segment area Yes, it is radians. But radians from a area of a circle sector not a segment. The result is that I get a redicously narrow angle.
 July 1st, 2013, 11:20 AM #6 Math Team     Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 234 Re: Circle segment area Post your calculations please so that we can check them. If i now understand you correctly , $\frac{2A}{r^2} \= \ \theta \ - \ sin{\theta}$ You have A , you have r so now you want to solve for $\ \theta \$ in radians. Is that right? If that's right , you can only get an approximation , there is no way i know of to get an exact solution. There may be a different approach to get the height that i don't know about , you don't have the length of the chord , do you?
 July 1st, 2013, 10:31 PM #7 Newbie   Joined: Jun 2013 Posts: 6 Thanks: 0 Re: Circle segment area It is a "real life" scenario where a horizontal positioned vibrating tube is filled with a product, could be flour, or sugar. The tube transports the product, such as conveyour belt. I'm the programmer of the controling device. I know the dimenion of the tube. I know how much is poured into the tube. Due to regulations no sensors alowed in the setup. I have to provide a "gauge" that tells the height of the product in the tube. Since I know the amount of of product in the tube, I know the area of the circle segment. Since I know the dimensions of the tube I know the radius. Chord is unknown. I wanted to calculate the height of the product. Present to the operator. Not at a high accuracy. For the "curiosity" ...the height is required since experienced has learned us that above and below a certain productheight the product is changed in homogeniousity. This is to be avoided.
July 1st, 2013, 11:39 PM   #8
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Re: Circle segment area

Well since you don't need high accuracy then it's easy to get a result using trial and error. Here is an approach. First calculate

$\frac{2A}{r^2}$

Get a number for that. Then use the graph of $\ y \= \ \theta \ - \ sin{\theta}$

[attachment=0:1j832pdu]MSP2201f207geaebfh4f1800003f19938gg2h3h8c8.GIF[/attachment:1j832pdu]

That number you calculated? Locate it on the vertical axis , then move horizontally accross till you hit the graph , then drop vertically down to the horizontal axis and read the value. That is your $\theta$ and it is in RADIANS.

Confirm your work by substituting that value into the formula to see how accurate it is. Make sure your calculator is in RADIANS mode. Accuracy will depend on how well you have read the graph. If you can get $\theta$ to within 2 to 3 decimal places it may be adequate to use that value to calculate the height to within reason.

Post your calculations so that we may do them as well , in particular, post A and r.

Attached Images
 MSP2201f207geaebfh4f1800003f19938gg2h3h8c8.GIF (3.4 KB, 222 views)

 July 2nd, 2013, 03:54 AM #9 Newbie   Joined: Jun 2013 Posts: 6 Thanks: 0 Re: Circle segment area Urgh.. I will need a sharp chisel to get this into a PLC.
 July 2nd, 2013, 08:52 AM #10 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1039 Re: Circle segment area Well, why don't you go here: http://www.ajdesigner.com/phpcircle/cir ... _theta.php Easier that typing back and forth here Another good place: http://mathworld.wolfram.com/CircularSegment.html

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### i know the radius of a circle and i want to know where on the circle is a chord of a certain lenght

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