1. Cavalieri’s Principal with Volume of Prisms and Cylinders

2. Postulate Volume of a Cube
Volume equals side cubed

3. Congruent Polyhedron have the same volumes
Postulate
Congruent Polyhedron have the same volumes

4. You can add volumes that do not overlap
Postulate
You can add volumes that do not overlap

5. 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

6. 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.

7. Theorem Volume of a Prisms
Volume equals Base Area times Height
V=Bh
Base Area =
3 times 4 = 12
V=12(12)=144cm3

8. Theorem Volume of a Cylinder
Volume equals Base Area times Height
V=Bh
Let r= 3; h = 7