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Surface Area & Volume

Surface Area & Volume. OBJECTIVES Slices of 3-dimensional figures Nets of 3-D solids Lateral areas, surface areas,volumes of solids Properties of congruent & similar solids. 3-dimensional figures. You will use different math websites for visualizations of 3-D figures.

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Surface Area & Volume

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  1. Surface Area & Volume OBJECTIVES Slices of 3-dimensional figures Nets of 3-D solids Lateral areas, surface areas,volumes of solids Properties of congruent & similar solids

  2. 3-dimensional figures You will use different math websites for visualizations of 3-D figures. • Take time to use these sites to help explain the material. • Refer back to them for formulas, detailed diagrams, and rotations • If the links are blocked by your firewall, copy the URL & paste it in the address on your homepage • Bookmark them or add to ‘favorites’ while you’re in this course.

  3. Websites for 3-dimensional geometry http://www.mathsisfun.com/platonic_solids.html http://www.mathsisfun.com/geometry/index.html http://mathforum.org/alejandre/workshops/polyhedra.html http://mathforum.org/library/drmath/sets/high_geom.html http://www.houseof3d.com/pete/applets/graph/index.html

  4. Nets & surface areas • Nets are ‘flattened’ 3-D figures– it’s the pattern to make the shape by folding. • Refer to the text for vocabulary and diagrams as well as the websites • Add areas of all non-overlapping sections of the net for each polygon for surface area of figure. http://www.mathsisfun.com/platonic_solids.html

  5. Surface area of prisms & cylinders • Refer to the websites and your text for diagrams and vocabulary: bases, lateral edges, altitude, prism & cylinder • Lateral area is the surface area minus the bases • Surface area includes both bases Right cylinder Regular prism L.A. = Ph = 2 π r h S.A. = Ph+2π r2 = 2 π r h + 2π r2 L.A. = P h S.A. = P h + 2B

  6. Surface areas of pyramids & cones http://www.mathsisfun.com/geometry/pyramids.html • Refer to the websites and your text for diagrams and vocabulary: base, vertex, lateral faces & edges, altitude, and slant height. • Refer to these resources for formulas

  7. Volume of prisms & cylinders • Right prisms: Volume = B • h, where B = area of base & h = height • Right cylinder: Volume = B • h = π r 2h

  8. Volume of pyramids & cones • Volume of Right pyramids: V = • Volume of right cone: V = Cavalarieri’s Principle: 2 solids of same height & same cross-sectional area have the same volume.

  9. Surface area & volume of spheres • Refer to text for vocabulary • Surface Area = 4 π r 2 • Volume =

  10. Congruent & similar solids 2 solids are congruent if: 2 solids are similar: if ratio of 2 solids are a : b, then surface area ratio – a 2 : b2 volume ratio – a 3 : b3

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