11.2 and11.4 Surface Area and Volume Prisms

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11.2 and11.4 Surface Area and Volume Prisms

  1. 1. Chapter 11 Surface Area and Volume 11.2 and 11.4 S
  2. 2. Essential UnderstandingS You can analyze a 3D figure by using the relationship among its vertices, edges, and facesS To find the surface area of a 3D figure, find the sum of the areas of all the surfaces of the figureS You can find the volume of a prism or cylinder when you know its height and the area of its base
  3. 3. ObjectivesS Students will be able to S recognize polyhedra and their parts S Visualize cross sections of space figures S Find the surface area of a prism and a cylinder S Find the volume of a prism and the volume of a cylinder
  4. 4. PolyhedronS A space figure, or 3D figure whose surfaces are polygonsS Face: each polygonS Edge: segment formed by the intersection of two facesS Vertex: point where three or more edges intersect
  5. 5. Euler’s FormulaS # Faces + # Vertices = # Edges + 2
  6. 6. Cross SectionS The intersection of a solid and a plane.S A slice of the solid
  7. 7. What is the cross section formed?
  8. 8. PrismsS Prism: polyhedron with two congruent, parallel faces, called basesS Lateral faces: all the other faces
  9. 9. Prisms…S Right prism: the lateral faces are rectangles and a lateral edge is an altitudeS Oblique Prism: some or all of the lateral faces are nonrectangular.S (For this chapter, assume that a prism is a right prism unless otherwise stated)
  10. 10. LA and SA of a PrismS Lateral Area (LA): sum of the areas of the lateral faces S LA = phS Surface Area (SA): sum of the lateral area and the area of the two bases S SA = LA + 2B
  11. 11. What is the Surface Area?
  12. 12. What is the Surface Area? Lateral Area?
  13. 13. Volume of a PrismS Volume = Base times heightS V = Bh
  14. 14. CylinderS Two congruent, parallel bases that are circles
  15. 15. LA and SA of a CylinderS Lateral Surface Area (LA): circumference of the base and the height of the cylinder S LA = 2πr * h OR S LA = πdhS Surface Area (SA): Sum of the lateral surface area the two bases S SA = LA + 2B S SA = 2πrh + 2πr2
  16. 16. Volume of a CylinderS Volume = Base times heightS V = BhS V = πr2h
  17. 17. Composite Space FigureS 3D figure that is a combination of two or more simpler figuresS To find the volume of a composite space figure, add the volumes of the figures that are combined
  18. 18. HomeworkS Pg. 704S #10 – 20 even, 26 (8 problems)S Pg. 721S #6 – 20 even, 38 (9 problems)S 17 total problems

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