1. Objective: Cavalieri’s principle. Finding volume. Warm up 1. a.Sketch a horizontal cross-section of the rectangular prism. b.Find the its volume. Show work

2. 2. a.Sketch a vertical cross-section of the triangular prism. b.Find the volume. Show work.

3. Example 1 Are the volumes of the two solids formed by two stacks of quarters the same or different? Explain.

4. By Cavalieri’s principle, if the area of each cross-section at the same height is the same, and the heights of each solid are the same, therefore the two volumes are equal.

5. Example 2

7. 1

8. Cavalieri’s Principle: If every plane parallel to the two planes intersects both solids in cross-sections of equal area, then the volumes of the two solids are equal.

9. Example 3. A rectangular prism and a cylinder have the same height and the same volume. What is the length of the side of the prism’s square base?

10. Example 4 a.Sketch three horizontal cross-sections. b.Find the Volume.

11. Assignment Pg 533 #1-6, 11, 15, 16