3D Modeling with AR: Part 10 - Cereal Bowl Function Modeling!
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
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). [br][br]Given the dimensions of the cereal bowl above, [br][br]Determine the coordinates (x,y, z) of A, B, C, and D so that the given function [i]f[/i] 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 [i]f[/i] 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).