Coordinate system solids

Three solid figures that could be defined in cylindrical or spherical coordinates. In cylindrical coordinates (where *r* is distance to the *z*-axis), the figures can be described by

Region 1: 0 < *z* < 1, *z*^2 + *r*^2 < 2
Region 2: 0 < *z* < *r*, *z*^2 + *r*^2 < 2
Region 3: 0 < *z*, 1 < *r*, *z*^2 + *r*^2 < 2

It is useful for a multivariable calculus student to think about how to calculate triple integrals over these three regions using cylindrical or spherical coordinates.

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