Volumes of Solids of RevolutionThe Method of Shells
This Mathematica notebook provides the code to produce animations to illustrate the steps involved
DOWNLOAD the Mathematica notebook HERE.
Turn off spelling warning (merely a convenience).
Revolution axis is the yaxis.
Define the functions. In this case the region is bounded by two curves. Representation as a function of y
x interval: This needs to be modified specifically for the functions in your example.
Set the plotting range window and the viewpoint. These statements need to be modified to suit the functions
Plot x and y axes.
Establish the partition (7 in this example).
Define the "front" edges of the rectangles that generate the shells.
Define the surfaces of revolution.
The region is illustrated using an inscribed 50vertex polygon between the curves. The vertices are generated
Define the surfaces of revolution that construct the shells.
The surfaces will be displayed as Graphics3D primitives that have specific colorings.
The approximating shells are stored in a table.
The surfaces of revolution are generated by varying the value of theta in the SurfaceOfRevolution and
The following code shows the steps (with pauses between the major steps) in the approximation
process,
Mathematica code produced for Demos with Positive Impact (NSFDUE 9952306) by Converted by Mathematica May 19, 2002
