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Chapter 12 Notes

Chapter 12 Notes. 12.1 – Exploring Solids. A polyhedron is a solid bounded by polygons. Sides are faces , edges are line segments connecting faces, and vertices are points where the edges meet. The plural of polyhedron is polyhedra or polyhedrons.

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Chapter 12 Notes

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  1. Chapter 12 Notes

  2. 12.1 – Exploring Solids

  3. A polyhedron is a solid bounded by polygons. Sides are faces, edges are line segments connecting faces, and vertices are points where the edges meet. The plural of polyhedron is polyhedra or polyhedrons. A polyhedron is regular if all the faces are congruent regular polygons. A polyhedron is convex if any two points on its surface can be connected by a segment that lies entirely on the polyhedron (like with polygons) There are 5 regular polyhedra, called Platonic solids (they’re just friends). They are a (look at page 721): tetrahedron (4 triangular faces) a cube (6 square faces) octahedron (8 triangular faces) dodecahedron (12 pentagonal faces) icosahedron (20 triangular faces)

  4. http://personal.maths.surrey.ac.uk/st/H.Bruin/image/PlatonicSolids.gifhttp://personal.maths.surrey.ac.uk/st/H.Bruin/image/PlatonicSolids.gif

  5. Is it a polyhedron? If so, count the faces, edges, and vertices. Also say whether or not it is convex. No

  6. Euler’s Theorem: (Like FAVE two, or cube method) Edges = Sides/2 Find vertices of polyhedra made up of 8 trapezoids, 2 squares, 4 rectangles. Find vertices of polyhedra made up of 2 hexagons, 6 squares.

  7. The intersection of a plane crossing a solid is called a cross section. Sometimes you see it in bio, when they show you the inside of a tree, the circle you get when you slice a tree is called the cross section of a tree.

  8. 12.2 – Surface Area of Prisms and Cylinders

  9. Terms P  Perimeter of one base B  Area of base b  base (side) h  Height (relating to altitude) l  Slant Height TA  Total Area (Also SA for surface Area) LA  Lateral Area V  Volume

  10. A prism has two parallel bases. Altitude is segment perpendicular to the parallel planes, also referred to as “Height”. Lateral faces are faces that are not the bases. The parallel segments joining them are lateral edges. Prism Net View

  11. If the lateral faces are rectangles, it is called a RIGHT PRISM. If they are not, they are called an OBLIQUE PRISM. Altitude. Lateral edge not an altitude. OBLIQUE PRISM. RIGHT PRISM

  12. Lateral Area of a right prism is the sum of area of all the LATERAL faces. = bh + bh + bh + bh = (b + b + b + b)h = Ph LA Total Area is the sum of ALL the faces. = 2B + Ph TA

  13. Cylinder

  14. Find the LA, SA of this triangular prism. LA = SA = 8 4 3 5

  15. Find the LA, SA of this rectangular prism. LA = SA = 5 3 8

  16. Find the LA and TA of this regular hexagonal prism. If it helps to think like this. 10 4

  17. Find the LA, and TA of this prism. 24 in 30 in 6 in 10 in 8 in

  18. Find lateral area, surface area Height = 8 cm Radius = 4 cm Height = 2 cm Radius = .25 cm

  19. Find the Unknown Variable. SA = x 2 8 V = 2x x 4

  20. Find the Unknown Variable. SA = 40πcm2 Radius = 4 cm Height = h SA = 100πcm2 Radius = r Height = 4 cm

  21. 12.3 – Surface Area of Pyramids and Cones

  22. vertex Lateral edge Altitude (height) Slant height Lateral Face (yellow) Base (light blue)

  23. A regular pyramid has a regular polygon for a base and its height meets the base at its center.

  24. Lateral Area of a regular pyramid is the area of all the LATERAL faces. Total area is area of bases. TA = B + Pl b b b b b + + + + l l l l l (b b b b b) + + + + =Pl l

  25. Cone

  26. Find Lateral Area, Total Area of regular hexagonal pyramid. 10 in 16 in

  27. Find Lateral Area, Total Area of regular square pyramid. 13 cm 10 cm

  28. Find lateral area, surface area Find surface area. Units in meters. 6 8 Slant Height = 15 in. Radius = 9 in

  29. Find unknown variable 8 cm x cm Slant height 8 cm Radius = ? TA = 105cm2 Slant height 8 in Radius = ? TA = 48 πin2

  30. Pyramid height 8 in Slant height 2 cm 20 in 2 cm 12 in

  31. Look at some cross sections

  32. 12.1 – 12.3 – More Practice, Getting Ready for next week

  33. Find the length of the unknown side

  34. Find the area of the figures below, all shapes regular

  35. Find the area of the shaded part

  36. To save time, formulas for 12.4 are as follows:

  37. 12.4 – Volume of Prisms and Cylinders

  38. Altitude is segment perpendicular to the parallel planes, also referred to as “Height”. Volume of a right prism equals the area of the base times the height of the prism. = Bh V Prism

  39. The volume of an OBLIQUE PRISMis also Bh, remember, it’s h, not lateral edge Altitude. Lateral edge not an altitude. OBLIQUE PRISM. RIGHT PRISM

  40. Find the V of this regular hexagonal prism. 10 4

  41. Find the V of this triangular prism. V = 8 4 3 5

  42. Find Volume Height = 8 cm Radius = 4 cm Cylinder

  43. Circumference of a cylinder is 12π, and the height is 10, find the volume.

  44. Find the unknown variable.

  45. What is the volume of the solid below?

  46. What is the volume of the solid below? Prism below is a cube.

  47. 12.5 – Volume of Pyramids and Cones

  48. Cone 13 cm 10 cm Slant Height = 15 in. Radius = 9 in

  49. Circumference of a cone is 12π, and the slant height is 10, find the volume.

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