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## Solids of Revolution

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• Has anyone tried to graph the classic surface of Revolution problems from Calculus using GC? It seems like one should be able to see the region in the x-y
Message 1 of 4 , Oct 3, 2005
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Has anyone tried to graph the classic surface of Revolution problems from Calculus using
GC? It seems like one should be able to see the region in the x-y plane, and animate the
revolution to see the solid of revolution.

I can see the region by graphing:

x=(0 if y<((f(x) if y > g(x)) if a<x<b)

But I can't seem to get the revolution working. Any help would be appreciated.

Russ
• ... I m not sure exactly what the equation your graphing here is. I got a general formula for parameterized curves out of the book Modern Differential
Message 2 of 4 , Oct 5, 2005
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On Oct 3, 2005, at 12:45 PM, Russ and Lisa wrote:

> Has anyone tried to graph the classic surface of Revolution problems
> from Calculus using GC? It seems like one should be able to see the
> region in the x-y plane, and animate the revolution to see the solid
> of revolution.
>
> I can see the region by graphing:
>
> x=(0 if y<((f(x) if y > g(x)) if a<x<b)
>
> But I can't seem to get the revolution working. Any help would be
> appreciated.
>
> Russ

I'm not sure exactly what the equation your graphing here is. I got a
general formula for parameterized curves out of the book "Modern
Differential Geometry of Curves and Surfaces with Mathematica", 2nd ed.
Boca Raton, FL: CRC Press, by Alfred Gray, on page 457. It's in the
following attached file, which I also uploaded to the Files section (
http://groups.yahoo.com/group/GraphingCalcUsers/files/ ) at Files >
Calculus, Analysis > Surfaces of revolution.
• ... Here s an example with a rotating meridian: (Also posted in the Files section at Files Calculus, Analysis Surfaces of revolution.
Message 3 of 4 , Oct 5, 2005
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On Oct 3, 2005, at 12:45 PM, Russ and Lisa wrote:

> Has anyone tried to graph the classic surface of Revolution problems
> from Calculus using
> GC? It seems like one should be able to see the region in the x-y
> plane, and animate the
> revolution to see the solid of revolution.
>
> I can see the region by graphing:
>
> x=(0 if y<((f(x) if y > g(x)) if a<x<b)
>
> But I can't seem to get the revolution working. Any help would be
> appreciated.
>
> Russ

Here's an example with a rotating meridian:
• ... Maybe the following is more what you wanted. It shows a revolving slice going around inside the surface of revolution. Also uploaded to Files Calculus,
Message 4 of 4 , Oct 5, 2005
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On Oct 3, 2005, at 12:45 PM, Russ and Lisa wrote:

> Has anyone tried to graph the classic surface of Revolution problems
> from Calculus using
> GC? It seems like one should be able to see the region in the x-y
> plane, and animate the
> revolution to see the solid of revolution.
>
> I can see the region by graphing:
>
> x=(0 if y<((f(x) if y > g(x)) if a<x<b)
>
> But I can't seem to get the revolution working. Any help would be
> appreciated.
>
> Russ

Maybe the following is more what you wanted. It shows a revolving
"slice" going around inside the surface of revolution.
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