Rotating 2D Graphs about Lines to Create 3D Surfaces of Revolution in GeoGebra AR


Students & Teachers with ARCore by Google Installed on Your Devices:

Here's how you can create a 3D surface by rotating the graph of ANY function about the xAxis within GeoGebra's 3D Graphing Calculator app. (This screencast was recorded on an ACER Chrome Tab 10.) For more information re: getting started with GeoGebra Augmented Reality, click here.

Quick Demo

Now, press the AR button (lower right) to explore this within GeoGebra Augmented Reality! Once viewing in Augmented Reality, slide the slider slowly. You should see a surface of revolution form!

Here's what this surface looks like in GeoGebra Augmented Reality!

For further exploration:

Note: If interested, you can use this pre-made template that can be found here. Follow the directions on this page to open in the GeoGebra 3D Graphing Calculator on your device. 1) Instead of f(x) = 3, try typing (just the way you see it). Spin this graph about the xAxis. What kind of solid do you get? 2) Same direction as in (1), but do this time for . What do you get now? 3) Same direction as in (1), but do this time for . What does this look like? 4) What other kinds of 3D surfaces of revolution can we create this way? Let your creativity take you places!

Another demo: Modeling a bowl