Volumes of Solids of Revolution: The Disk Method
This Mathematica notebook provides code for visualization of the disk method for computing the volume of a solid of revolution. The examples involve revolving the region bounded between y =
f[x], x = a, and x = b revolved about the x-axis. Further, we assume that f[x] is nonnegative over the interval.
n is the number of disks.
Dissect the region into rectangles that determine the disks. Radii are determined by the function evaluated at the midpoint of each subinterval.
Show the radii; then draw the rectangles.
Plot the surface.
Generate the cross sections.
Generate the cylinders' edges.
Show approximating disks together.
Show surface and disks.
DOWNLOAD THE MATHEMATICA NOTEBOOK: diskmethod.nb
Mathematica notebook by
Converted by Mathematica September 23, 2001 Last updated 5/19/2006 DRH