Title: Assignment: (Task) Tennis Ball Packaging
Course: HBUHSD Geometry Resource Course

Estimated Time: 60 - 90 minutes + Discussion

Teacher Notes: This task is inspired by the derivation of the volume formula for the sphere. If a sphere of radius 1 is enclosed in a cylinder of radius 1 and height 2, then the volume not occupied by the sphere is equal to the volume of a “double-naped cone” with vertex at the center of the sphere and bases equal to the bases of the cylinder. This can be seen by slicing the figure parallel to the base of the cylinder and noting the areas of the annular slices consisting of portions of the volume that are inside the cylinder but outside the sphere are the same as the areas of the slices of the double-naped cone (and applying Cavalieri’s Principle). This almost magical fact about slices is a manifestation of Pythagorean Theorem. We see it at work in Part 6 of this task. The other parts of the task are exercises in 3D-visualization, which build up the spatial sense necessary to work on Part 6 with understanding. The visualization required here is used in calculus, in connection with procedures for calculating volumes by various slicing procedures.

Geometric Measurements - Tennis Ball Task.pdf

Teacher Commentary and Answer Key