Cavalieri's Principle
Learn how Cavalieri's Principle helps you compare volumes of 3D shapes with the same height and cross-sectional area. Let's get started! 🚀
Video Lesson
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Flashcards
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🛎️ Cavalieri’s Principle in Real Life
- Imagine two stacks made from the same number of slices.
- If each slice has the same area, the stacks have the same volume.
- Rearranging the slices does not change the volume of the stack.
🛎️ What Is Cavalieri’s Principle?
- Two solids can look different but still have the same volume.
- They must have the same height.
- They must have the same cross-sectional area at every level.
🛎️ Use Cavalieri’s Principle to Find Volume
- At each height, a tilted prism has the same cross-sectional area as an upright prism with the same base area.
- So by Cavalieri’s principle they have the same volume, and you can use V = base area × height.
🛎️ Checking Equal Volume Using Cavalieri’s Principle
- Compare the height and the cross-sectional area at matching levels.
- If they match all the way up, the solids have equal volume.
Practice Questions
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Interactive Activity
Cavalieri’s Principle: Volume depends on base area and height, regardless of slant
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