# From 2D to 3D Modeling: It's Easier Than You Think!

Topic:
Cylinder

## Math Teachers:

For students that have studied various classes of functions (linear, quadratic, square root, trigonometric), YOU CAN engage them in 3D modeling activities (& challenges) within GeoGebra Augmented Reality! In this screencast below, note the two surface equations and . If we were to replace z with y, we would have the equations of the top and bottom halves (respectively) of 2 semicircles with radius = 4 units we would typically have students graph in the coordinate plane. Yet instead - here, we write z as a function of x and restrict the domain of this surface to be , or . More info can be found below the screencast.

## Quick (Silent) Demo

Yet where did this domain restriction come from? That part is easy. Before building the model, we measured the radius of this cylindrical coffee maker. Here, r = 10.5 cm and the height of this cylinder = 4.6 cm. Since we chose 4 UNITS in GeoGebra Augmented Reality to represent 10.5 cm = radius, we need to determine how many units represent the height of this cylinder. Thus, . And upon solving, we get ? = 1.75 units. Since we chose the plane y = 0 to split this cylindrical lateral area in half, this surface needs to extend 1.75u / 2 = 0.876 units in both the positive y-direction and negative y-direction. Hence, the need for the domain restriction . And this simple level of proportional reasoning is a task that MANY STUDENTS can do by the time they study various classes of functions in high school. Building 3D mathematical models of real-world objects IS a task MANY STUDENTS CAN DO after studying various classes of functions. So why restrict modeling to only be within the (2D) coordinate plane?