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 |