A typical problem you're often given is to find the volume of the solid of revolution formed by rotating the area between 2 function graphs about a horizontal axis (y = some number) or vertical axis (x = some number). [br][br]Here, you can use GeoGebra Augmented Reality within GeoGebra's 3D Graphing Calculator to CREATE & EXPLORE such a surface of revolution within GeoGebra Augmented Reality!

1) Open up GeoGebra 3D Graphing Calculator on your non-iOS device that has [b][color=#9900ff]ARCore by Google[/color][/b] [br] installed on it. [br][br]2) Click on the 3 horizontal bars (upper left). Select [b]OPEN[/b]. [br][br]3) To rotate the area between 2 function graphs about a HORIZONTAL AXIS (y = some number), type in [br] the code [b]BZWTCPfd[/b]. (It IS case sensitive). [br][br] To rotate the area between 2 function graphs about a VERTICAL AXIS (x = some number), type in [br] the code [b]wendqwg7[/b]. (It IS case sensitive). [br][br]4) Once the resource loads, scroll upwards in the Algebra view (bottom) within this app. [br][br]5) The greater (higher) function is f (top most bar). You can modify this. (See pic below).[br] The lesser (lower) function is h. You can modify this. [br] [color=#ff0000][b]a = lower limit of integration (modifiable)[/b][/color][br] [color=#1e84cc][b]b = upper limit of integration (modifiable). [/b][/color][br] n = the angle at which you will soon rotate this region (between the 2 graphs) about the line. [br] [color=#9900ff][b]c = the y-value of the horizontal line about which you will rotate (if you chose a horizontal axis).[br] o = the y-value of the vertical line about which you will rotate (if you chose a vertical axis). [/b] [/color] [br] s = the shading level of the surface (w/s = 0 being no shade and s = 1 = fully shaded). [br] [br][br] Leave the rest of the objects alone, and you'll be all set! Happy exploring!