Solid Figure for Triple Integral Practice

This is a model of the solid region defined by

y^2 < z < 9-(x^2+y^2)

It is useful practice for multivariable calculus students to think about how one might set up the integration bounds for such a solid. In particular, the cross-sections are not easy to visualize and there are no planar faces.

To interface with a physical vertical z-axis, there is an option to have a hole down the middle.

This model was designed as part of the Manipulative Calculus project at Harvard University.