# GeoGebra 3D: Warm Up

In the GeoGebra 3D app below, the black segment is parallel to the xAxis. Suppose we were to rotate (spin) this black segment 360 degrees (fully) about the xAxis. What would be the resulting surface of revolution formed by doing so? Write your guess/conjecture below. ﻿

## Slide the slider n all the way to the right to create a surface of revolution. Note the black segment is parallel to the xAxis.

Take a look at the GeoGebra applet below. In this applet, the black segment has one of its endpoints on the xAxis. Suppose we were to rotate (spin) this black segment 360 degrees (fully) about the xAxis. What would be the resulting surface of revolution formed by doing so? Write your guess/conjecture below. Then, test your conjecture by sliding the black slider (named n) all the way to the right.

## Slide the slider n all the way to the right to create a surface of revolution. Note the black segment has one endpoint that lies on the xAxis.

The GeoGebra applet below shows the surface of revolution formed by rotating the graph of the function f(x) = sin(x) (from x = 0 to x = 4) about the xAxis. Notice how this surface looks like a fish. How can we modify the function f above (upper left) to create a fish with an OPEN MOUTH? Try it! How can we modify the function f above (upper left) to create 2 kissing fish? Try it!