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

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Presentation transcript:

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. 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.

Websites for 3-dimensional geometry

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.

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 L.A. = Ph = 2 π r h S.A. = Ph+2π r 2 = 2 π r h + 2π r 2 L.A. = P h S.A. = P h + 2B Right cylinderRegular prism

Surface areas of pyramids & cones 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

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

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.

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

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 : b 2 volume ratio – a 3 : b 3