Curriculum placement

Geometry. This describes the skill, not a learner estimate.

Cross-sections and solids of revolution

Relate plane slices and rotations of plane figures to three-dimensional solids

Problem types

Sections and solids of revolution

Builds on

Cross-sections of solids
Volume of cylinders, cones, and spheres · Earlier idea
Volumes of cylinders, cones and spheres are explained as solids of revolution.

Leads to

Volumes of cylinders, cones, pyramids, spheres · See it applied
A rotated rectangle, right triangle or semicircle sweeps out a cylinder, cone or sphere, whose volume formula gives the volume.

Related skills

Cavalieri's principle · Related idea
A solid of revolution is built from circular cross-sections, and Cavalieri compares solids by their cross-sections.
Conic sections and their equations · Related idea
Rotating a parabola about its axis gives a paraboloid, and slicing a cone gives the conic curves.

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