2. Oh no, here we go again. Theorem 11-5: Cavalieri’s Principle If two space figures have the same height and the same cross- sectional area at every level, then they have the same volume.

3. Example: 3 2 3 22 6 A=lw A=3  2 A=6 units 2 A=lw A=3  2 A=6 units 2 Since they all have the same area, then they have the same volume. A=.5b h A=.5  6  2 A=6 units 2

4. Theorem 11-6: Volume of a Prism The volume of a prism is the product of the area of the base and the height of the prism. V=B area h

5. Example: 3 2 3 22 6 A=lw A=3  2 A=6 units 2 A=lw A=3  2 A=6 units 2 A=.5bh A=.5  6  2 A=6 units 2 10 10 10 V=Bh V=6  10 V=60 units 3 V=6  10 V=60 units 3 V=6  10 V=60 units 3

6. Theorem 11-7: Volume of a Cylinder The volume of a cylinder is the product of the area of the base and the height of the cylinder V=B area h V=  r 2 h

7. Example: 8 cm 3 cm V=  r 2 h V=  (3cm) 2 (8cm) V=  (72cm 3 ) V=804.2cm 3

8. Volume of Composite Space Figure Find the volume of each figure and then add the volumes together.

9. Example: 12 in. 4 in. 17 in. 12 in. 4 in. 11 in. 4 in. 6 in. V =  r 2 h ( )/2 V = (  ·6 2 ·4)/2 V = 226in 3 V = lwh V = 12  4  11 V = 528in 3 V=226in 3 +528in 3 V=754in 3