# Rotating about X-AXIS: Creating Surfaces of Revolution in GGB AR

- Author:
- Tim Brzezinski

- Topic:
- Surface

Consider the function .
In calculus, we often end up studying the solid of revolution formed by rotating the graph of a function about the X-AXIS.
In GeoGebra's 3D Graphing Calculator, this is actually quite easy to do. The silent screencast below illustrates how easy this actually is.

## How to Create a Surface of Revolution Formed by Rotating ANY Function Graph about X-AXIS

## Try it yourself before moving forward! Note: You don't have to use the function illustrated above. You can use ANY FUNCTION!

However, GeoGebra's Augmented Reality app currently only allows users to plot to surfaces of the form
. That is,

*z*need to be written as a function of*x*and*y*.**So let's first consider this:**For the surface of revolution shown below,**cross sections**parallel to the yz-plane are**CIRCLES whose radius is****.**To see this in action, move the**LARGE BLUE POINT**to the LEFT in the applet below. Note how these cross sections are always circles. The equation of such a circle is .## Move the LARGE BLUE POINT to the LEFT. Note cross sections are CIRCLES with radius = f(x).

Upon solving the equation above for

*z*, we obtain and . Thus, given this, any surface of revolution formed by rotating the graph of a function about the X-AXIS can be consider to be 2 SURFACES PUT TOGETHER:**z = a surface with POSITIVE OUPUTS (top half)****z = a surface with NEGATIVE OUTPUTS (bottom half).****
**Thus, for , we obtain
**= blue surface shown below.
** **= pink surface shown below. **

## Now let's see what this looks like in GeoGebra Augmented Reality. TRY IT and EXPLORE!

Note how this surface above resembles a vase.

**What other 3D solids can students model with only 2 surface functions within GeoGebra Augmented Reality?**