Calculating the surface area of an ellipse?

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Offline Donnah

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Calculating the surface area of an ellipse?
« on: 06/05/2004 15:28:24 »
Hey everyone!
Donnah's son again [:D]
New question, although a bit more mathmatical in nature.
In my calculus class, we have been debating a bit about how to find the surface area of an ellipse.
I have a pretty good theory as to how to get the perimeter, but still the SA eludes me.  Anyone Know?
Thanks
-Steve
« Last Edit: 30/06/2004 09:07:20 by Exodus »
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Offline Dan B

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Re: Calculating the surface area of an ellipse?
« Reply #1 on: 06/05/2004 16:34:16 »
Integrate your circumference from 0 to 2pi.
 

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Offline Ylide

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Re: Calculating the surface area of an ellipse?
« Reply #2 on: 07/05/2004 18:38:34 »
Or, if line integral aren't your thing, you can do it with a basic cartesian equation of the ellipse.

Center the ellipse on the origin and write it as an equation, X^2/a^2 + Y^2/b^2 = 1.  (where a is the X-axis radius and b is the y-axis radius)  Solve for Y = f(x)  and you have the equation for one half of the ellipse.  Integrate the equation f(x) over the length in the x-axis and you have the area under the top half of the ellipse.  Now double it, and there's your answer.



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Offline chris

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Re: Calculating the surface area of an ellipse?
« Reply #3 on: 14/05/2004 04:46:05 »
Wow, nicely done !

Chris

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Offline Ylide

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Re: Calculating the surface area of an ellipse?
« Reply #4 on: 30/06/2004 14:30:07 »
A year and a half of calculus had to be good for something.



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