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MathGroup Archive 1997

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Re: Volumes using Cylindrical Shells

  • To: mathgroup at smc.vnet.net
  • Subject: [mg6469] Re: [mg6453] Volumes using Cylindrical Shells
  • From: "Preferred Customer" <sherman.reed at worldnet.att.net>
  • Date: Sun, 23 Mar 1997 13:22:52 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

(*An example, Assume we want the volume generated bounded by a line y = 2x,
and the line y = 3, rotated around the x axis.*)
<<Graphics`FilledPlot`
FilledPlot[{2x,3},{x,0,1.5}]
(*The shell radius is x.  The length of the shell is 
2*Pi*x.  The thickness of the shell is dx.
The height of the shell is 3 - y, or 3 - 2x.
We integrate from x = 0 to x = 1.5.*)
Integrate[2*Pi*x*(3-2*x),{x,0,1.5}]
(*volume of cone is (1/3)*base area*height or*)
N[(1/3)*Pi*(3/2)^2*3]

above is an example that will execute in 3.0.
The basic idea is to create a shell volume.
length times height times thickness.
in thie above example length is 2*Pi*x, the heighth is 3 - 2x and the
thickness is dx.
We integrate from x = 0 to x = 1.5, or said differently, we
sum from x - 0 to x = 1.5 with dx approaching zero.

most high school calc books are pretty good here.

sherman reed

----------
> From: MadMacree <mine at address.net>
To: mathgroup at smc.vnet.net
> To: mathgroup at smc.vnet.net
> Subject: [mg6453] Volumes using Cylindrical Shells
> Date: Friday, March 21, 1997 9:59 PM
> 
> I haven't been able to get Mathematica 3 to find the volume of curves
> rotated around an axis using cylindrical shells.
> 
> What is the easiest way to do this?
> -----------------------
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