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Chapter 12 – Surface Area and Volume of Solids

Chapter 12 – Surface Area and Volume of Solids. REVIEW. Section 12.1– Space Figures and Nets. Section 12.1. Polyhedron – a 3-D figure whose surfaces are polygons. Face – individual polygon of the polyhedron. Edge – is a segment that is formed by the intersection of two faces.

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Chapter 12 – Surface Area and Volume of Solids

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  1. Chapter 12 – Surface Area and Volume of Solids REVIEW Section 12.1– Space Figures and Nets

  2. Section 12.1 Polyhedron – a 3-D figure whose surfaces are polygons. Face – individual polygon of the polyhedron. Edge – is a segment that is formed by the intersection of two faces. Vertex – is a point where three or more edges intersect. REVIEW

  3. Section 12.1 Net – a 2-D pattern that you can fold to form a 3-D figure. Euler’s Formula – the number of faces (F), vertices (V), and edges (E) of a polyhedron are related by the formula: F + V = E + 2 REVIEW

  4. CUBE: Net Drawing REVIEW

  5. CUBE: 3-Dimensional Faces REVIEW Edge Vertex

  6. CYLINDER: Net Drawing REVIEW

  7. CYLINDER: 3-Dimensional Faces REVIEW Edge

  8. TRIANGULAR PRISM: Net Drawing REVIEW

  9. TRIANGULAR PRISM: 3-Dimensional REVIEW Edge Faces Vertex

  10. RECTANGULAR PRISM: Net Drawing REVIEW

  11. RECTANGULAR PRISM: 3-Dimensional Faces REVIEW Edge Vertex

  12. HEXAGONAL PRISM: Net Drawing REVIEW

  13. HEXAGONAL PRISM: 3-Dimensional Faces REVIEW Edge Vertex

  14. TRIANGULAR PYRAMID: Net Drawing REVIEW

  15. TRIANGULAR PYRAMID: 3-Dimensional REVIEW Slant Height Altitude

  16. SQUARE PYRAMID: Net Drawing Slant Height REVIEW

  17. SQUARE PYRAMID: 3-Dimensional Slant Height REVIEW

  18. HEXAGONAL PYRAMID: Net Drawing REVIEW

  19. HEXAGONAL PYRAMID: 3-Dimensional Slant Height REVIEW Altitude

  20. Chapter 12 – Surface Area and Volume of Solids Section 12.2 – Surface Areas of Prisms and Cylinders

  21. Section 12.2 Prism – is a polyhedron with exactly two congruent, parallel faces. Bases – two congruent, parallel faces of a prism. Lateral Faces – additional faces of a prism. Altitude – is a perpendicular segment that joins the planes of the bases.

  22. Section 12.2 Height – the length of the altitude. Right Prism – the lateral faces are rectangles and a lateral edge is the altitude of the prism. Oblique Prism – at least one lateral face is not a rectangle. Lateral Area – is the sum of the area of the lateral faces.

  23. CUBE: 3-Dimensional BASE LATERAL FACE

  24. RECTANGULAR PRISM: 3-Dimensional BASE LATERAL FACE

  25. TRIANGULAR PRISM: 3-Dimensional LATERAL FACE BASE

  26. HEXAGONAL PRISM: 3-Dimensional BASE LATERAL FACE

  27. OBLIQUE PRISM: 3-Dimensional BASE LATERAL FACE ALTITUDE

  28. Section 12.2 Surface Area – the sum of the lateral area and the two bases. Theorem 10-1 – the lateral area of a right prism is the product of the perimeter of the base and the height.L.A. = phThe surface area of a right prism is the sum of the lateral area and the area of the 2 bases.S.A. = L.A. + 2B

  29. Section 12.2 Cylinder – is a three-dimensional figure with exactly two congruent, parallel faces. Bases – two congruent, parallel faces of a cylinder are circles. Altitude – is a perpendicular segment that joins the planes of the bases.

  30. CYLINDER: 3-Dimensional BASE

  31. OBLIQUE CYLINDER: 3-Dimensional BASE ALTITUDE

  32. Section 12.2 Surface Area – the sum of the lateral area and the two circular bases. Theorem – the lateral area of a right prism is the product of the circumference of the base and the height of the cylinder. L.A. = 2πrh orL.A. = πdh The surface area of a right prism is the sum of the lateral area and the area of the 2 bases. S.A. = L.A. + 2B or S.A. =2πrh + 2πr2

  33. Chapter 12 – Surface Area and Volume of Solids Section 12.3 – Surface Areas and Pyramids and Cones

  34. Moving from Prisms/Cylinders to Pyramids/Cones

  35. Section 12.3 Pyramid – is a polyhedron in which one face can be any polygon and the other faces are triangles that meet at a common vertex. Bases – the only face of a pyramid that is not a triangle. Lateral Faces – triangles of pyramid. Vertex of a pyramid – the point where all lateral faces of a pyramid meet.

  36. Section 12.3 Altitude – is a perpendicular segment from the vertex to the plane of the base. Height – the length of the altitude (h). Regular Pyramid – a pyramid whose base is a regular polygon and whose lateral faces are congruent isosceles triangles. Slant Height – is the length of the altitude of a lateral face of a pyramid. Lateral Area – is the sum of the area of the congruent lateral faces.

  37. TRIANGULAR PYRAMID: 3-Dimensional Slant Height Altitude

  38. SQUARE PYRAMID: 3-Dimensional Slant Height

  39. HEXAGONAL PYRAMID: 3-Dimensional Slant Height Altitude

  40. Section 12.3 Surface Area – the sum of the lateral area and the area of the base. Theorem – the lateral area of a regular pyramid is the half the product of the perimeter of the base and the slant height.L.A. = ½ plThe surface area of a regular pyramid is the sum of the lateral area and the area of the base.S.A. = L.A. + B

  41. Section 12.3 Cone – is a “pointed” like a pyramid, but its base is a circle. Right Cone – the altitude is a perpendicular segment from the vertex to the center of the base. Bases – the only circle on a cone. Vertex of a cone – the only distinctive point on the object.

  42. Section 12.3 Altitude – is a perpendicular segment from the vertex to the plane of the base. Height – the length of the altitude (h). Slant Height – is the distance from the vertex to a point on the edge of the base. Lateral Area – is ½ the perimeter (circumference) of the base times the slant height.

  43. CONE: Net Drawing

  44. CONE: 3-Dimensional

  45. Section 12.3 Surface Area – the sum of the lateral area and the area of the base. Theorem – the lateral area of a right cone is the half the product of the circumference of the base and the slant height.L.A. = ½ 2rl orrl The surface area of a right cone is the sum of the lateral area and the area of the base.S.A. = L.A. + B

  46. Chapter 12 – Surface Area and Volume Section 12.6 – Surface Area and Volumes of Spheres

  47. Section 12.6 Sphere Set of all points equidistant from a given point. C

  48. Section 12.6 Surface Area of a Sphere S = 4πr 2 C

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