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Solids Of Revolution


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#1 TZ250

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Posted 04 February 2010 - 03:28 PM

In class we're working on solids of revolution. How do I make the CP330 draw something like that? I can rotate a 3D function, and shade the difference between two functions, but I don't know how to revolve a function.

Example: The region bounded by y=(square root of X) , y=2X+1, X=1 and X=4.

How do I draw that? (in solid form)

#2 ASTRO491K

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Posted 06 February 2010 - 02:06 AM

Keep in mind that unlike shading the difference between two functions in the x-y plane, solids of revolution are just that, solids. That requires that you plot the 3d surface equivalent of the solid of revolution, for example rotataing the semi-circle y=sqrt(1-x^2) about the x axis is equivalent to plotting the 3d surface x^2+y^2+z^2=1, i.e., z=+/-sqrt(1-x^2-y^2). I hope this reply is helpful because to my knowledge there is no built in function for displaying the rotated solid of revolution. Of course I could be wrong.

In class we're working on solids of revolution. How do I make the CP330 draw something like that? I can rotate a 3D function, and shade the difference between two functions, but I don't know how to revolve a function.

Example: The region bounded by y=(square root of X) , y=2X+1, X=1 and X=4.

How do I draw that? (in solid form)



#3 Kilburn

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Posted 06 February 2010 - 09:24 PM

Is this what you need?

Posted Image

In the 3D Graph app, press the "Z=" button so it turns into "Xst", that will allow you to graph 3D parametric equations. If you want to rotate a function around an axis and see what it looks like, here's the formula:

X(s,t) = cos(t) * f(s)
Y(s,t) = sin(t) * f(s)
Z(s,t) = s

Where f is the function you want to revolve. Just look at the above picture, I did that with the square root function. Just modify smin and smax in the axis properties if you want a wider range.

#4 ASTRO491K

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Posted 07 February 2010 - 03:39 AM

Wow, that is really nice Kilburn. Could you then plot an additional surface, say the plane z=1-x-y to show how it intersects with the paraboloid that you already have? That would be really really super!


Is this what you need?

Posted Image

In the 3D Graph app, press the "Z=" button so it turns into "Xst", that will allow you to graph 3D parametric equations. If you want to rotate a function around an axis and see what it looks like, here's the formula:

X(s,t) = cos(t) * f(s)
Y(s,t) = sin(t) * f(s)
Z(s,t) = s

Where f is the function you want to revolve. Just look at the above picture, I did that with the square root function. Just modify smin and smax in the axis properties if you want a wider range.



#5 Kilburn

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Posted 07 February 2010 - 08:11 PM

Wow, that is really nice Kilburn. Could you then plot an additional surface, say the plane z=1-x-y to show how it intersects with the paraboloid that you already have? That would be really really super!


Nope, as far as I know, you can't even draw several surfaces at once. :(

#6 ASTRO491K

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Posted 07 February 2010 - 11:38 PM

Nope, as far as I know, you can't even draw several surfaces at once. :(


Hi Kilburn, me again. Isn't there some way to generate and store a surface, and then generate the second surface and store it, and then simply display both? If that was possible, it would be totally awesome!




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