Volume by Shells in Calculus

[libman]

Hi all,

I was wondering if there is a way to model volumes by shells with Auotgraph?

All the best,
Libman

[Simon]

Hi libman,

"Kindof" is the best answer I can give you.  In Autograph you can either do a volume of revolution of the area under y = f(x) around y = k where you specify k OR you can do a volume of revolution about any straight line.  In the latter case the volume is not calculated.  

So to show a volume by shells (but not calculate it):

1. Plot y = f(x)
2. Select your curve > right-click > Find Area to find the area between two points
3. Plot x = 0
4. Select Slow Plot
5. Select the area and the line x = 0
6. Right-click > Find Volume...

Hope this helps,

Simon

[libman]

Works perfectly as a visual tool! Would be great to see the volumes values - BUT, fantastic as far as I am concerned. I can teach the theory much more easily with the 3D plot.

Might be best to clarify that a person needs to be working in 3D mode and also understand how to rotate a region about the x axis or a line parallel to the x axis first.

To all: See http://www.autograph-maths.com/inaction/td/Volumes.htm

Miss communicating with you SImon.

Thanks,
Libman,
aka G.Landry

[slake60]

I need to find the volume for y=f(x) rotated about x=0...how do I do that please?  Also, we do not have the Plot as 2D function in the 3D window when we want to plot the y=f(x).  Please advise

Many thanks

[Simon]

Dear slake60,

First of all you need to check whether the version of Autograph you have is new enough to support Volumes of Revolution. Go to Help > About, you need Version 3.2 or above.

If you have the a recent version then to rotate about x = 0 do the following:

1. Enter an equation y = f(x)
2. Select "Plot as 2D equation" and click OK
3. Select the curve, right-click Find Area.
4. Enter an equation x = 0.
5. Select the area and the line x = 0, right-click and select Volume.

Hope that helps,

Simon