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? > ----------------------- > ** Specter ** | "My God, It's full of Stars." 2010: The Year We Made Contact > specter at geocities.com | "I think therefore I am." Rene Descartes > specter at nassau.cv.net | "Believe in yourself." Louis Pasteur > http://www.geocities.com/WallStreet/1475/index.html