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Space Figures & Nets, Surface Areas of Prisms & Cylinders

Space Figures & Nets, Surface Areas of Prisms & Cylinders. Chapter 10 Sections 1 & 3. Faces. Edge. Vertex. Vocabulary. Polyhedron. a 3D figure whose surfaces are polygons. Face. the polygons in a polyhedron. Edge. a segment that is formed by the intersection of two faces. Vertex.

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Space Figures & Nets, Surface Areas of Prisms & Cylinders

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  1. Space Figures & Nets, Surface Areas of Prisms & Cylinders Chapter 10 Sections 1 & 3

  2. Faces Edge Vertex Vocabulary Polyhedron a 3D figure whose surfaces are polygons Face the polygons in a polyhedron Edge a segment that is formed by the intersection of two faces Vertex the point where three or more edges intersect

  3. Vocabulary Net a 2D pattern that you can fold to form a 3D figure Cube a polyhedron with six faces, each of which is a square

  4. Drawing Nets Draw a net for the following figure. Label the net with its dimensions. Pg 115 #1-9

  5. Euler’s Formula The numbers of faces (F), Vertices (V), and edges (E) of a Polyhedron are related by the formula: F + V = E + 2 Example Find the number of edges on a solid with 6 faces and 8 vertices. Leonhard Euler (1707-1783) 12 Edges

  6. Practice F + V = E + 2 Use Euler’s Formula to Solve A polyhedron with 12 vertices and 30 edges has how many faces? Pg 116 #10-12

  7. lateral edge Vocabulary Prism a polyhedron with exactly two congruent, parallel faces Bases the two congruent, parallel faces of a polyhedron Lateral Faces the other faces of a polyhedron

  8. Lateral Area of a Cylinder The product of the circumference of the base and the height Pg 119 #1-6 10 in. 12 in.

  9. Surface Area of a Cylinder The sum of the lateral area and the areas of the two bases 10 in. Pg 120 #13-15 12 in.

  10. Lateral Area of a Prism The product of the perimeter of the base and the height p = perimeter of the base h = height

  11. Surface Area of a Prism The sum of the lateral area & the areas of the two bases Area of a Triangle Formula Triangle Base Pg 119 #7-12

  12. Summary Today I learned to: ________________________________. I do this by: ________________________________. This is related to: ________________________________.

  13. Remember: HW is due next class! NO make-up work is allowed. Homework Workbook 10.1: p.115-116 #1-12 10.3: p.119-120 #1-15

  14. Surface Areas of Pyramids & Cones, Volumes of Prisms & Cylinders Chapter 10 Section 4 & 5

  15. Review Find the surface area of the following figures: 10 in. 12 in.

  16. Vocabulary Pyramid – a polyhedron in which one face (the base) can be any polygon and the other faces (the lateral faces) are triangles that meet at a common vertex Altitude – the perpendicular segment from the vertex to the plane of the base Regular Pyramid – a pyramid whose base is a regular polygon and whose lateral faces are congruent isosceles triangles Slant Height – the length of the altitude of a lateral face of the pyramid

  17. Lateral Area of a Regular Pyramid The sum of the areas of the congruent lateral faces P = perimeter of the base = slant height Step 2: Plug in to the formula Step 1: Find the slant height ? 11.7 4 8 Pg 121 #7-9

  18. Surface Area of a Regular Pyramid The sum of the lateral area and the area of the base = slant height B= area of the base P = perimeter of the base Step 1: Find the slant height ? 10.4 Step 2: Plug into the formula 10 3 6 Pg 122 #10-12 6

  19. Lateral Area of a Cone Half the product of the circumference of the base and the slant height = slant height Step 1: Find the slant height ? 6.4 Step 2: Plug into the formula Pg 121 #1-3

  20. Surface Area of a Cone The sum of the lateral area and the area of the base = slant height Step 1: Find the slant height ? 5 Step 2: Plug into the formula 4 3 Pg 121 #4-6

  21. Volume of a Cylinder The product of the area of a base and the height of the cylinder 10 in. 12 in. Pg 123 #1 – 6

  22. Volume of a Rectangular Solid The product of the area of a base and the height of the prism B = Area of the base h = height of the prism Pg 123 #7, 9, 10, 11

  23. 10 in 8 in 8 in 8 in Volume of a Triangular Prism The product of the area of a base and the height of the prism B = Area of the base h = height of the prism 43 Step 1: Find the triangle height Step 2: Plug into the formula 8 in 8 in o 60 h = ? h = 43 Pg 122 #8, 12

  24. Summary Today I learned to: ________________________________. I do this by: ________________________________. This is related to: ________________________________.

  25. Remember: HW is due next class! NO make-up work is allowed. Homework Workbook 10.4: p.121-122 #1-12 10.5: p.123-124 #1-15

  26. Volumes of Pyramids & Cones, Surface Areas & Volumes of Spheres Chapter 10 Sections 6 & 7

  27. Review Find the surface area of the following figures: 10 in. 12 in.

  28. Review Find the volume of the following figures: 10 in. 12 in.

  29. Volume of a Pyramid The product of the area of the base and the height of the pyramid 4 Pg 125 #1 – 6

  30. Volume of a Cone The product of the area of the base and the height of the cone Pg 125 #7 – 12

  31. Surface Area of a Sphere Four times the product of the area of pi and the square of the radius of the sphere 5 Pg 127 #1 – 6

  32. Volume of a Sphere Four-thirds the product of pi and the cube of the radius of the sphere 5 Pg 127 #7 - 10

  33. Summary Today I learned to: ________________________________. I do this by: ________________________________. This is related to: ________________________________.

  34. Remember: HW is due next class! NO make-up work is allowed. Homework Workbook 10.6: p.125-126 #1-12 10.7: p.127-128 #1-10

  35. Areas & Volumes of Similar Solids Chapter 8 Section 8

  36. Review Find the lateral area of the pyramid P = perimeter of the base = slant height Step 1: Find the slant height ? 11.7 Step 2: Multiply with the perimeter of the base 4 8

  37. Review Find the surface area of the cone = slant height Step 1: Find the slant height ? 5 Step 2: Plug into the formula 4 3

  38. Review Find the volume of the cone

  39. Review Find the surface area of the sphere 5

  40. Vocabulary Similar Solids: Have the same shape and all their corresponding dimensions are proportional Similarity Ratio: The ratio of corresponding linear dimensions of two similar solids.

  41. Identifying Similar Solids Are the following prisms similar? If so, give the similarity ratio 3 6 2 3 4 6

  42. Practice Pg 129 #3 – 6 Are the following cylinders similar? If so, give the similarity ratio 6 in. 5 in. 12 in. 11 in.

  43. Areas and Volumes of Similar Solids Theorem If the similarity ratio of two similar solids is a:b, then (1) the ratio of their corresponding areas is a2:b2 (2) the ratio of their volumes is a3:b3

  44. Finding the Similarity Ratio Two cubes with volumes of 729cm3 and 1331cm3. Two similar prisms with surface areas of 144m2 and 324m2.

  45. Using a Similarity Ratio #1 Two paint cans have the areas 1019cm2 and 425cm2. The volume of the small can is 1157cm3. Find the volume of the large can. #2 Pg 129 #7 – 9

  46. Using a Similarity Ratio #1 The volumes of two similar solids are 128m3 and 250m3. The surface area of the larger solid is 250m2. What is the surface area of the smaller solid? #2 Pg 130 #10 – 12

  47. Summary Today I learned to: ________________________________. I do this by: ________________________________. This is related to: ________________________________.

  48. Remember: HW is due next class! NO make-up work is allowed. Homework Workbook 10.8: p.129-130 #1-12

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