MATLAB routine diskmethod.m
GENERATE SURFACES of REVOLUTION by rotating y = f(x) about the x-axis.
This is to be used as a visual aid for showing the notions behind the
generation of surfaces of revolution and leading to the calculus integral
expression for the volume of such surfaces.
This is an interactive program that takes as input
expression for y = f(x),
domain interval [a,b],
and the number slices to be taken across the domain. (MAX 10 slices.)
With this information the curve is sketched in the xy-plane and radii
shown for the slices to generated. A slice near the middle of the region
is then colored to show a strip of area. Next we show the cross sections
of the slices in three dimensions and the cylinder disk generated by the
colored strip. This is followed by the generation of cylindrical disks
corresponding to each of the slices. The sum of the volumes of these
cylindrical disks would yield an approximation the volume of the surface
of revolution. Finally the entire surface of revolution is displayed.
Once this surface has been generated, it can be rotated using the
MATLAB tools appearing in the toolbar.
A user must click in the input boxes and then type the requisite data.
No check for validity of the data entered is made. If there is an error
MATLAB will generate a message on the text screen when the data is processed.
If you click in an input box and then press enter default data will appear.
The default values are f(x)= x2 over [0,1] with 10 slices.
Throughout this demonstration utility buttons for HELP, RESTARTing,
and QUITing are available.
The routine does no volume computations, rather can be used to motivate
the calculus formula for the volume.
AUXILIARY ROUTINES: addaxes, addaxes3, cylind1 by D.R.Hill
By: David R. Hill
Philadelphia, Pa. 19122
Lila F. Roberts
Department of Mathematics
Georgia College & State University
Milledgeville, GA 31061
Constructed 3/1/2002 Last updated 5/19/2006 DRH