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.

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Presentation transcript:

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

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

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.

Example 2

1

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.

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?

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

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