Calculus › Section O · Multiple integrals › Topic O.7
Triple integrals in cylindrical and spherical coordinates
Round solids deserve round coordinates: cylindrical and spherical systems turn spheres, cones and cylinders into constant limits, at the small price of a volume element that remembers the curve.
In this topic
- Round solids want round coordinates
- Cylindrical coordinates: polar plus height
- Worked example: a cylinder capped by a paraboloid
- Spherical coordinates: distance and two angles
- Why the spherical element carries sin φ
- Worked example: the volume of a ball
- Worked example: the ice-cream cone
- Choosing the coordinate system
- Common mistakes to avoid
- Key takeaways
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Standards: Beyond AP