Fubini's Theorem Lesson

These two solid figures, Region E and Region F, are meant to be part of a multivariable calculus lesson on solid regions in three dimensions and Fubini's Theorem and Cavalieri's Principle. Students are given the two sets of inequalities below, and must first identify which model corresponds to which set of inequalities.

| Inequalities 1       | Inequalities 2 |
|----------------|-----------------|
| 0 < *x* < 1-*z* | 0 < *x* < *z*+1 |
| *z*^2 < *y* < 1 | 0 < *y* < (*z*-1)^2 |
| 0 < *z* | 0 < *z* |

Students then use calculus to compare the volumes of the two models.

This page is meant to complement the paper "3D Printed Manipulatives in a Multivariable Calculus Classroom" which will appear in PRIMUS.