3D Modeling with AR: Part 10 - Cereal Bowl Function Modeling!

GOAL: Build this CEREAL BOWL

GOAL: Build this CEREAL BOWL

Here's one means we can actively engage our Algebra 1 & Geometry students in this task:

DIMENSIONS OF BOWL ABOVE

DIMENSIONS OF BOWL ABOVE

Slide the SPIN slider slowly. Doing so will spin the graph of function f around the xAxis to create a surface of revolution. This graph is said to be a CROSS SECTION of this bowl.

MATH TEACHERS:

We addressed the 2 task questions below in the video above. Feel free to use these questions to serve as a guide for students as they engage with this.

TASK 1:

Let's position this bowl in 3-space above so that (0,0,0) = origin lies at the center of the smaller circle (bottom of the bowl). Given the dimensions of the cereal bowl above, Determine the coordinates (x,y, z) of A, B, C, and D so that the given function f is a cross section of this bowl. (Note: the z-coordinate of any point on the gray plane is 0. Thus, all these points will have a z-coordinate of 0.)

TASK 2:

Determine the equation of function f with any domain restrictions (that need to take place) so that the black function graph shown is literally the lateral height of this bowl (frustum).

Quick (Silent) Demo