Understanding Volume of Prisms and Cylinders: Theorems and Principles
Explore the volume of prisms and cylinders using postulates and theorems. Learn about Cavalieri’s Principle, calculating volume, and solving problems.
Understanding Volume of Prisms and Cylinders: Theorems and Principles
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Presentation Transcript
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/
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
Homework Page 746 – 748 # 13 – 39 odd
