Students use calculus (solid of revolution) in both Cartesian and Parametric form to determine the volume of an ellipse when it is rotated around the axis to form an ellipsoid (football). Students also use arc-length to check measurements.
The solid of revolution for an ellipse is much more straight forward than students may think. One of the most common ellipsoids is an AFL football. Sherrin, the official supplier of AFL footballs manufacture a range of different sizes. Students determine the volume of selected footballs from their website, however there is a twist, and its not a torpedo, more of a drop punt. Football sizes are provided as circumference measurements, so students need to use the arclength to generate greater accuracy.
- Solid of revolution
- Arc length
- Cartesian form
- Parametric form
About the Lesson
An AFL football is almost perfectly elliptical. Students start by determining the equation to an ellipse the best models the shape and then rotate this relation around the x axis to determine the volume of the ellipsoid (football). Upon completion, students measure an actual football to compare theoretical calculations with the practical result. Students can improve on the accuracy by using actual specification for the small and large circumference, therefore requiring calculations of arc length. Who would have thought that there would be so much mathematics in a football?