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.