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As calculus teachers, we stand at the intersection of mathematical theory and practical problem-solving. One topic that often perplexes students is Volumes of Solids of Revolution. These three-dimensional shapes emerge from the elegant dance of curves and rotations, yet their intricacies can leave even the most diligent learners scratching their heads.
But fear not! In this blog post, I will share several free and user-friendly websites and programs that can help students visualize the 3D solids created.
The best websites/programs are the ones that are user-friendly, allow the user to enter their own function, and rotate an area around any vertical or horizontal axis.
Be sure to check out: Free Websites for Creating Solids with Known Cross Sections
Top Pick
- My personal preference is to download a FREE software called Autograph onto my laptop https://autograph.completemaths.com/
- This is available on Windows only.
- It will only rotate around a horizontal axis.
- Read more about Autograph here: hoffmath.com/2020/05/autograph.html
- Watch a demo video: youtu.be/hOjo4Wd55lI
Second Choice:
- www.shodor.org/interactivate/activities/FunctionRevolution
- This site does not have as many of the features of Autograph and is a little less user-friendly than Autograph, but it does allow the user to rotate around a vertical axis.
Third Choice:
Geogebra is a very powerful and FREE software. Anyone can make an "interactive worksheet" that has its own URL and can be viewed by anyone. Here are some of my favorites:- https://www.geogebra.org/m/BZWTCPfd
- can rotate around any vertical or horizontal asymptote (made by Tim Brzezinski)
- it's not easy to change the scale of the graph
- https://www.geogebra.org/m/fd9kfvrh
- can only rotate around the x- or y-axis (made by Przemysław Kajetanowicz)
- https://www.geogebra.org/m/zBRtUVfR
- can only rotate around the x- or y-axis (made by Andreas Lindner)
Honorable mention:
- https://www.geogebra.org/m/hhRJQyz9
- disk method that shows the actual disks (made by Tim Brzezinski)
- https://www.geogebra.org/m/fy3c4pyf
- washer method that shows the actual washers (made by Tim Brzezinski)
You may also be interested in:
What to Teach in Non-AP Calculus
How to graph a Volume of Revolution with Autograph Software
The Best Graphing Software for Your Math Classroom.
