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Cavalieri’s Principal with Volume of Prisms and Cylinders. Postulate Volume of a Cube. Volume equals side cubed. Postulate. Congruent Polyhedron have the same volumes. Postulate. You can add volumes that do not overlap. Cavalieri’s Principle.
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Postulate Volume of a Cube Volume equals side cubed
Postulate Congruent Polyhedron have the same volumes
Postulate You can add volumes that do not overlap
Cavalieri’s Principle • Cavalieri’s Principle essentially states that if two prisms have the property that all corresponding cross sections have the same area, then those prisms have the same volume. The CDs stacks have the same Volume http://mrhonner.com/2011/04/06/cds-and-cavalieris-principle/
Cavalieri’s Principle Historical Note Bonventura Francesco Cavalieri (1598 – 1647) Cavalieri’s work with indivisibles was a precursor to the development of calculus. His method of indivisibles is what is now known as Cavalieri’s Principle.
Theorem Volume of a Prisms Volume equals Base Area times Height V=Bh Base Area = 3 times 4 = 12 V=12(12)=144cm3
Theorem Volume of a Cylinder Volume equals Base Area times Height V=Bh Let r= 3; h = 7
