# 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.

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
##### Pros

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

• 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