Surface Area

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 youre
  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 its 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 p r h S.A. Ph2p r2 2 p r h
2p 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 p r 2 h

8
Volume of pyramids cones

• Volume of Right pyramids
• V
• Volume of right cone
• V
• Cavalarieris 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 p 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