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11.4 Volumes of Prisms and Cylinders

11.4 Volumes of Prisms and Cylinders. 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. Example:. 2. 2. 2. 3. 3. 6. A=lw. A=lw. A=.5b h.

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11.4 Volumes of Prisms and Cylinders

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  1. 11.4 Volumes of Prisms and Cylinders

  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: 2 2 2 3 3 6 A=lw A=lw A=.5b h A=32 A=32 A=.5 62 A=6 units2 A=6 units2 A=6 units2 Since they all have the same area, then they have the same volume.

  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=Bareah

  5. Example: 2 2 2 3 3 6 A=lw A=lw A=.5bh A=32 A=32 A=.562 A=6 units2 A=6 units2 A=6 units2 V=Bh 10 10 10 V=610 V=610 V=610 V=60 units3 V=60 units3 V=60 units3

  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=Bareah V=r2h

  7. Example: 3 cm V=r2h V=804.2cm3 8 cm V=(3cm)2(8cm) V=(72cm3)

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

  9. Example: V=226in3+528in3 ( )/2 V = r2h V=754in3 V = (·62·4)/2 V = 226in3 17 in. 6 in. 4 in. 4 in. 12 in. V = lwh 11 in. V = 12411 4 in. V = 528in3 12 in.

  10. Assignment page 469 all

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