Unit 10 · Measurement and Three-Dimensional Geometry

10.7Volume of Prisms and Cylinders

Quick Answer

Volume of a prism: V = Bh (base area × height). Volume of a cylinder: V = πr²h. Both use the same principle: volume = base area × height.

Essential Question

Why do prisms and cylinders share the same volume formula structure V = Bh, and how does Cavalieri's Principle justify this?

Learning Goals

  • 1State Cavalieri's Principle.
  • 2Apply the volume formula V = Bh for any prism.
  • 3Apply the volume formula V = πr²h for a cylinder.
  • 4Find the volume of oblique prisms and cylinders.

Key Vocabulary

Volume

The number of cubic units needed to fill a three-dimensional solid.

Cavalieri's Principle

If two solids have the same height and the same cross-sectional area at every level, they have the same volume.

Oblique solid

A solid in which the lateral edges are not perpendicular to the bases.

Full lesson content coming soon

Worked examples, guided practice problems, a workbook, quiz, and downloadable PDF resources will be added to this lesson in Phase 2. The learning goals and vocabulary above reflect the complete lesson scope.