Here's how you can create a 3D surface by rotating the graph of ANY function about the xAxis within [url=https://play.google.com/store/apps/details?id=org.geogebra.android.g3d]GeoGebra's 3D Graphing Calculator app[/url]. (This screencast was recorded on an ACER Chrome Tab 10.) [br][br]For more information re: getting started with GeoGebra Augmented Reality, [url=https://www.geogebra.org/m/jhcywuqw]click here[/url].

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

[b]Note[/b]:[br][br]If interested, you can use this pre-made template [url=https://www.geogebra.org/m/qbxbcmqw#material/yt22anmh]that can be found here[/url]. [br]Follow the directions on this page to open in the [color=#1e84cc]GeoGebra 3D Graphing Calculator[/color] on your device. [br][br]1) Instead of f(x) = 3, try typing [math]f\left(x\right)=x,0\le x\le4[/math] (just the way you see it). Spin this graph about the [br] xAxis. What kind of solid do you get? [br][br]2) Same direction as in (1), but do this time for [math]f\left(x\right)=x,2\le x\le4[/math]. What do you get now? [br][br]3) Same direction as in (1), but do this time for [math]f\left(x\right)=0.5x^2,0\le x\le2[/math] . What does this look like? [br][br]4) What other kinds of 3D surfaces of revolution can we create this way? [br] Let your creativity take you places!