Use Cavalieri’s Principle to Compare Aquarium Volumes

This Use Cavalieri’s Principle to Compare Aquarium Volumes activity & project also includes:

Learners are designing a stunning new water feature for an aquarium, but they soon discover that more than just a pretty home for their fishy friends is required.  From calculating the volume of a composite shape through the abstract development of cross-sectional area formulas, these seemingly simple problems have some serious geometric chops! A capstone application of Cavalieri's principle ties the whole activity together, relating volumes of different shapes in a satisfying way.

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CCSS: Designed
Instructional Ideas

  • Aquarium filling could be simulated using physical models before abstract calculations are performed
  • Could be linked with a science unit or lesson on Cavalieri's Principle
  • Possible introduction problem to larger project on solid volumes and cross-sectional areas or volumes of rotation
Classroom Considerations

  • Those not familiar with Cavalieri's principle will need an explanation of that key concept
  • Student worksheet not separated from teacher notes and answer key

  • Multi-step problem really encourages mathematical thinking and development of logical reasoning
  • Application of volume formulas in an interesting context

  • Right margin cut off by up to several letters in some places
  • Described as leading students toward discovering the formula for the volume of a sphere, but this is not developed in the lesson
Common Core