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March 17th, 2011, 02:33 PM  #1 
Newbie Joined: Mar 2011 Posts: 7 Thanks: 0  Area for this shape
Hey I'm wondering if there is a equation or formula for finding the area to this certain shape. I've searched everywhere, and cannot find one. I've also tried to work it, but can't seem to figure it out. Thanks in advance! [attachment=0:2a7l3flc]odd cresent oval.png[/attachment:2a7l3flc] 
March 17th, 2011, 03:28 PM  #2 
Senior Member Joined: Jul 2010 From: St. Augustine, FL., U.S.A.'s oldest city Posts: 12,193 Thanks: 504 Math Focus: Calculus/ODEs  Re: Area for this shape
Do you happen to know if the arcs are circular, elliptical, parabolic, hyperbolic, etc.?

March 17th, 2011, 06:09 PM  #3 
Newbie Joined: Mar 2011 Posts: 7 Thanks: 0  Re: Area for this shape
Thank you so much for replying. What I'm trying to do is calculate the area of a half open open ball valve like this one. Can you see the shape I am trying to calculate the area of? Does that help? [attachment=0:vfg4ap75]150pxBall.PNG[/attachment:vfg4ap75] 
March 18th, 2011, 12:27 AM  #4  
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March 18th, 2011, 02:56 PM  #5 
Newbie Joined: Mar 2011 Posts: 7 Thanks: 0  Re: Area for this shape
Yes, the radius for the fully open valve is 0.5 inches. Could you explain how to calculate the area using that info? Could I use the equation for the area of an ellipse? Area = Pi*A*B

March 18th, 2011, 03:38 PM  #6  
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March 18th, 2011, 03:50 PM  #7  
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,842 Thanks: 1068 Math Focus: Elementary mathematics and beyond  Re: Area for this shape Quote:
http://en.wikipedia.org/wiki/Circular_segment#Area R = 1/2, ? = ?  2arctan(1/2), (radian measure used) Area = 2 * 1/8 * (?  2arctan(1/2)  4/5) ? 0.3535743589. You may need to account for the curvature of the ball.  
March 18th, 2011, 04:58 PM  #8  
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We can prove that the area is an ellipse, and it's quite simple, if you want to I can do this. Try to think in that problem in another view: You're rotating a circle about a diameter and you don't change your look. The diameter(now major axis) will be always constant, the the minor axis will decrease. Rotating the sphere you'll get a family of ellipses and when you completely open the valve you'll get a straight vertical segment(a degenerated ellipse), right?  
March 18th, 2011, 05:11 PM  #9 
Global Moderator Joined: Oct 2008 From: London, Ontario, Canada  The Forest City Posts: 7,842 Thanks: 1068 Math Focus: Elementary mathematics and beyond  Re: Area for this shape
A simple diagram should suffice to show the area is not an ellipse.

March 18th, 2011, 05:21 PM  #10  
Guest Joined: Posts: n/a Thanks:  Re: Area for this shape Quote:
Like this.  

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