The Volume of Prisms and Cylinders and Cavalieri’s Principle

Young mathematicians examine area of different figures with the same cross-sectional lengths and work up to volumes of 3D figures with the same cross-sectional areas. The instruction and the exercises stress that the two figures do not have to be the same but do need to have the same heights.

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CCSS: Designed
Instructional Ideas

  • Use two different solids that would have the same cross sectional areas, such as a cylinder and prism
Classroom Considerations

  • Some pupils may have a problem with recognizing equal areas, especially if the shapes are different
  • Parallel slices are the same as cross sections
  • The tenth module in a 14-part series
Pros

  • Provides concrete examples of Cavalieri's Principle
  • The proof is not a complicated rigorous proof; it is more informal and can be understood at this grade level
Cons

  • None