Volume by Shells in Calculus - Printable Version
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Volume by Shells in Calculus - libman - 04-02-2008 03:25 AM
I was wondering if there is a way to model volumes by shells with Auotgraph?
All the best,
Re: Volume by Shells in Calculus - Simon - 05-02-2008 12:59 PM
"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,
Re: Volume by Shells in Calculus - libman - 25-01-2010 09:54 AM
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.
Re: Volume by Shells in Calculus - slake60 - 26-01-2010 04:28 PM
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
Re: Volume by Shells in Calculus - Simon - 01-02-2010 07:38 PM
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,