11.3 and11.5 Surface Area and Volume Pyramids

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11.3 and11.5 Surface Area and Volume Pyramids

  1. 1. Chapter 11 Surface Area and Volume 11.3 and 11.5 S
  2. 2. Essential UnderstandingS To find the surface area of a 3D figure, find the sum of the areas of all the surfaces of the figureS The volume of a pyramid is related to the volume of a prism with the same base and heightS The volume of cone is related to the volume of a cylinder with the same base and height
  3. 3. ObjectivesS Students will be able to S Find the surface area of a pyramid and a cone S Find the volume of a pyramid and of a cone
  4. 4. PyramidsS Pyramid: polyhedron in which one face (the base) can be any polygon and the other faces (lateral faces) are trianglesS Vertex: top of pyramidS Slant height: length of the altitude of a lateral face of the pyramidS Assume a pyramid is a regular pyramid unless otherwise stated
  5. 5. LA and SA of PyramidsS Lateral Area (LA): sum of the areas of the congruent lateral faces S Half the product of the perimeter and the slant height S LA = ½ plS Surface Area (SA): add the area of the base to the lateral area. S SA = LA + B S SA = ½ pl + BS When the slant height is not given you must find it first in order to find the LA or the SA
  6. 6. What is the Surface Area
  7. 7. What is the lateral area?
  8. 8. Volume of a PyramidS V = 1/3 Bh
  9. 9. ConeS Base is a circleS Right Cone: altitude is a perpendicular segment form the vertex to the center of the baseS Height is the altitudeS Slant Height: distance from the vertex to a point on the edge of the base
  10. 10. LA and SA of a ConeS Lateral Area (LA): half the product of the circumference of the base and the slant height S ½ * 2πr * l = S πrlS Surface Area (SA): sum of the lateral area and the base S LA + B S πrl + πr2
  11. 11. What is the surface area in terms of pi?
  12. 12. Volume of a ConeS V = 1/3BhS V = 1/3 π r2 h
  13. 13. HomeworkS Pg. 713S #10 – 22 even, 28 (8 problems)S Pg. 729S #6 – 18 even, 30 (8 problems)S 16 problems total

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