Graphing Solids of Revolution ~ AP Calc

[Josh Mize]

I am looking for an easy way to model solids of revolution to a group of Calc AB students using the 3D graphing component of the Nspire. It could just be something that I can't wrap my head around (you may now chuckle if you got the pun), but if I know y=f(x), is there an easy way to translate that function into z=f(x,y) for me to be able to enter this in?

Thanks in advance for your help.

Josh Mize

[Steve Arnold]

Z1(x,y)= real(sqrt(f1(x)^2 - y^2))

 

With best wishes,

Steve

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[Sean Bird]

There are two recent TI-math activities that will be of interest to this topic

http://education.ti.com/calculators/timath/US/Activities/?sa=5023&d=1007 

(The tns files have been available on our TI-Nspire google group website for awhile   https://sites.google.com/site/tinspiregroup/assignments )

The answer to your question can be found on pg 4.2 of Solid of Rev.tns

If you have f1(x) graphed. You can get half of the graph that is rotated about the x axis if you do z1(x,y)=real(sqrt((f1(x))^2-y^2)

To also answer your question - this is hard. I would say it is not easy to get the equation in 3D for a solid of revolution. It really livens things up when you want to rotate around x=2 or something else.

But for what we do in AP Calc, these two files can really be of assistance in teaching the key things and helping students get a visual.  Rotating the 3D graph on the right around left to right is quite satisfying. 

- Sean Bird

Covenant Christian High School

Indianapolis, IN

[Sean Bird]

Oh yes, and one more special trick that we won't need to use when we graph 3D in parametric with OS3.2 ...

You need to change the document setting from real to complex. See this image:

(For the record, I'm not a big fan of Float6. I prefer Float. That is one of the first things I tell my students. It helps them get some of their Webassign questions correct in AP Physics.)

On Thu, Mar 22, 2012 at 11:39 AM, Sean Bird <covena...@gmail.com> wrote:

There are two recent TI-math activities that will be of interest to this topic

http://education.ti.com/calculators/timath/US/Activities/?sa=5023&d=1007 

(The tns files have been available on our TI-Nspire google group website for awhile   https://sites.google.com/site/tinspiregroup/assignments )

The answer to your question can be found on pg 4.2 of Solid of Rev.tns

If you have f1(x) graphed. You can get half of the graph that is rotated about the x axis if you do z1(x,y)=real(sqrt((f1(x))^2-y^2)

 z2(x,y) = -z1(x,y)