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MathGroup Archive 1997

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Re: Volumes using Cylindrical Shells

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

(*An example, Assume we want the volume generated bounded by a line y = 2x,
and the line y = 3, rotated around the x axis.*)
(*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.*)
(*volume of cone is (1/3)*base area*height or*)

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>
To: mathgroup at
> To: mathgroup at
> 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?
> -----------------------
> **  Specter  ** | "My God, It's full of Stars." 2010: The Year We Made
> specter at | "I think therefore I am." Rene Descartes
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