In the GeoGebra 3D app below, the [b]black segment [/b]is parallel to the [b][color=#ff0000]xAxis[/color][/b]. [br]Suppose we were to rotate (spin) this [b]black segment[/b] 360 degrees (fully) about the [b][color=#ff0000]xAxis[/color][/b].[br]What would be the resulting surface of revolution formed by doing so? [br][br]Write your guess/conjecture below.
Take a look at the GeoGebra applet below. [br][br]In this applet, the [b]black segment [/b]has one of its endpoints on the [b][color=#ff0000]xAxis[/color][/b]. [br]Suppose we were to rotate (spin) this [b]black segment[/b] 360 degrees (fully) about the [b][color=#ff0000]xAxis[/color][/b].[br]What would be the resulting surface of revolution formed by doing so? [br][br]Write your guess/conjecture below. Then, test your conjecture by sliding the black slider (named [b]n[/b]) all the way to the right.
The GeoGebra applet below shows the surface of revolution formed by rotating the graph of the[br]function [b]f(x) = sin(x) (from x = 0 to x = 4)[/b] about the [color=#ff0000][b]xAxis[/b][/color]. Notice how this surface looks like a fish. [br][br]How can we modify the function f above (upper left) to create a fish with an [b]OPEN MOUTH? [/b]Try it! [b][br][/b]How can we modify the function f above (upper left) to create[b] 2 kissing fish[/b]? Try it!