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12.4 Volume of Prisms and Cylinders

12.4 Volume of Prisms and Cylinders. Definition. Volume of a Solid- The number of a cubic units contains in its interior. Volume Postulates . Post 27- The volume of a cube is the cube of the length of its side or v=s Post 28- If two polyhedra are congruent then they have the same volume

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12.4 Volume of Prisms and Cylinders

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  1. 12.4 Volume of Prisms and Cylinders

  2. Definition • Volume of a Solid- The number of a cubic units contains in its interior.

  3. Volume Postulates • Post 27- The volume of a cube is the cube of the length of its side or v=s • Post 28- If two polyhedra are congruent then they have the same volume • Post 29- The volume of a solid is the sum of the volumes of all its non-overlapping parts.

  4. Volume Theorems • Theorem 12.6: Cavalieri’s principle- if two solids have the same height and the same cross-sectional area at every level then they have the same volume • Theorem 12.7: Volume of a prism- the volume V=Bh where B is the area of a base and H is the height.

  5. Theorems continued • Theorem 12.8: Volume of a cylinder- The volume V of a cylinder is V=Bh=3.14r h, where B is the area of a base, H is the height, and R is the radius of a base.

  6. Example 1Find the Volume of the Cylinder V=1/2 of 13 x 6 x 3.14 V=6.5 x 6 x V=39 x V=122.46 Cubic Feet.

  7. Example 2Find the Volume of the Right Prism • V=LWH • V=12.7 x 6 x 15.2 • V=1158.24cm

  8. Assignment • P. 746-748 7-9, 13-18 skip 15, 26-32 even, 46

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