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  • 1. Chapter 12 - Surface Area & Volume of Solids
    • Objectives:
    • Identify types of solids
    • Calculate surface area & volume of:
    • Prisms
    • Pyramids
    • Cylinders
    • Cones
    • Spheres
  • 2. 12.4 & 5 Volume of Prisms & Cylinders & Pyramids & Cones Objectives: Find Volume of prisms cylinders pyramids cones
  • 3. What is volume?
    • The volume of a solid is the number of cubic units contained in its interior.
    • Volume is measured in cubic units, such as cubic meters (m 3 )
  • 4. Volume Postulates
    • Volume of a Cube
      • The volume of a cube is the cube of the length of its side, or V = s 3
    • Volume Congruence
      • If 2 polyhedra are congruent, they have the same volume
    • Volume Addition Postulate
      • The volume of a solid is the sum of the volumes of all its nonoverlapping parts.
  • 5. Example
    • If a box is 5 inches long, 3 inches wide, and 4 inches, high, what is the volume?
    • 5*3*4 inches cubed
    • 60 “ 3
  • 6. Cavalieri’s Principle
    • If 2 solids have the same height and the same cross-sectional area at every level, then they have the same volume.
    • Look at the picture on p. 744
  • 7. Volume of a Prism
    • The volume V of a prism is V = Bh,
      • where B is the area of a base,
      • and h is the height.
  • 8. Volume of a Cylinder
    • The volume V of a cylinder is V = Bh =πr 2 h
      • where B is the area of a base,
      • h is the height,
      • And r is the radius of the base.
  • 9. Do example 2, p. 744
  • 10. Volume of a Pyramid
    • The volume V of a pyramid is V = 1/3 Bh
      • where B is the area of a base,
      • And h is the height
  • 11. Volume of a Cone
    • The volume V of a cone is V = 1/3 Bh = 1/3 πr 2 h
      • where B is the area of a base,
      • h is the height,
      • And r is the radius of the base.
  • 12. Do Example 1, p. 752
    • And example 2, p. 753
    • Then do worksheets