Practice question · Match the pairs
Match each solid to the natural coordinate system for its triple integral.
- Rectangular box
- Cylinder
- Sphere
- Cone
- Spherical (, , )
- Cylindrical or Spherical
- Cartesian (x, y, z)
- Cylindrical (r, , z)
Hints
- Match the coordinate symmetry to the shape of the solid.
- A sphere and a cylinder call for different angular variables.
Show the answer
- Rectangular box → Cartesian (x, y, z)
- Cylinder → Cylindrical (r, , z)
- Sphere → Spherical (, , )
- Cone → Cylindrical or Spherical
Why
Matching coordinates to geometry simplifies the limits and integrand.
Practise Triple Integrals
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