Volume of Revolution

Disks and Shells

One of the standard integration problems is to find the volume of a solid of revolution.  For a curve y=f(x) that runs from x=a to x=b, if we rotate around the axis y=AR, the lines from the curve to the axis of rotation becomes a disc.  The cross sections have area DiskArea(x) = pi*(f(x)-AR)2.  The volume of the region is Volume Integral.


If we rotate the other way, around the y axis, the line from the top curve to the bottom curve becomes a shell of height (f(x)-g(x) and radius x.  The volume of the region is Volume Integral.


These applets were designed as by modifying an applet from a demo by Tom Banchoff at Brown University.  It is used with permission.   Go to the Banchoff Applet Help page.

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Last updated By Mike May, S.J. ,  October 11, 2006.