The site contains a collection of tutorials and animations (Flash and Java) on finding volumes of solids of revolution. This set of materials should be helpful for students who are visual learners.
Type of Material:
Tutorial and animation
This site can be used for instructor generated demonstrations or for student explorations.
A Java enabled browser, Flash player and/or JAVA plug-in
Identify Major Learning Goals:
To help students better understand the process of finding volumes of solids of revolution.
Target Student Population:
Students in the second semester or second quarter of Calculus.
Prerequisite Knowledge or Skills:
First semester or first quarter of Calculus
Evaluation and Observation
This site contains tutorials and animations that help the user understand the basic concepts behind finding the volume of solids of revolution using the disk or washer methods. Examples include revolving about the x-axis and the y-axis and revolving the area below a curve and above the x-axis and the area bounded by two curves. Students could quickly and efficiently visualize the solid obtained by rotating a graph around a straight line. Colorful animations lead a user step by step revealing both the visual construction behind the method and formal integration techniques. Examples provided help with understanding the main ideas of the method.
All the examples are polynomials. It would be helpful to see an example that involves a more complicated curve. It would also be helpful to see an example of two curves that cross each other.
Potential Effectiveness as a Teaching Tool
This site is an excellent supplement to any calculus textbook. It could be easily used for an in-class demonstration or as a part of self-guided study of the disk or washer methods of finding volumes. The site should be really helpful to students who are visual learners.
In the example that uses similar triangles the step that involves setting up the ratios is omitted. Many students will get lost at this point. The explanation of the integration refers to “Formulas #1, #2, and #3 from the table of integrals.” Most students do not use integral tables for integrals and all students should know how to integrate polynomials by the time they get to volumes with discs and washers.
Ease of Use for Both Students and Faculty
Provided that all the necessary plug-in are installed, the site is very easy to use; the software issues do not get in the way of the mathematics. Any student should be able to work through each of these animated tutorials without any help from the instructor.
The site would definitely benefit from a better design. Some of the applets require a LiveMath plug-in that may take an effort to find and install. It would be nice to have a “back” button on the demonstrations.