1. Ch 4 Measuring Prisms and Cylinders

2. Area of a Rectangle To find the area of a rectangle, multiply its length by its width. A = l x w

3. How do you find the area So, the area is 8.36 cm 2.

4. Area of a Triangle To find the area of a triangle, multiply its base by its height, then divide by 2. Remember the height of a triangle is perpendicular to its base. The formula for the area of a triangle can be written:

5. How do you find the area. Substitute b = 12 and h = 3. So, the area is 18 m 2.

6. Watch Brainpop: Area of Polygons http://www.brainpop.com/math/geometryandme asurement/areaofpolygons/preview.weml http://www.brainpop.com/math/geometryandme asurement/areaofpolygons/preview.weml

7. Area of a Circle To find the area of a circle, use the formula: A =  r 2 A =  r 2 where r represents the radius of the circle Recall that  is a non-terminating and a non- repeating decimal number. So, any calculations involving  are approximate. You need to use the  function on your calculator to be more accurate – 3.14 is not accurate enough.

8. How do you find the Area Use A =  r 2. Substitute r = 6 ÷ 2 = 3. So, the area is about 28 mm 2.

9. Circumference of a Circle The perimeter of a circle is named the circumference. The circumference is given by: C =  d or C = 2  r (Recall: d = 2r)

10. Find the circumference of the circle. The circumference of the circle is about 22 cm.

11. Find the radius of the circle. The circumference of a circle is 12.57 cm To find the radius of the circle, divide the circumference by 2 . The radius of the circle is about 2 cm.

12. Watch Brainpop: Circles http://www.brainpop.com/math/geometryandme asurement/circles/preview.weml http://www.brainpop.com/math/geometryandme asurement/circles/preview.weml http://www.youtube.com/watch?v=lWDha0wqbcI

13. Try It Workbook pg 74 – 75 Puzzle Package

14. Activating Prior Knowledge: Words to Know CongruentRectangleHexagon NetTriangleRegular Dodecagon BaseRight PrismEquilateral Triangle PolygonTriangular PrismIsosceles Triangle PolyhedronCubeSurface Area FaceCompassVolume EdgeRegular PyramidCapacity VertexCylinderPi PrismPentagon

15. Watch Brainpop: Review http://www.brainpop.com/math/numbersandoperatio ns/pi/preview.weml http://www.brainpop.com/math/numbersandoperatio ns/pi/preview.weml http://www.brainpop.com/math/geometryandmeasur ement/polygons/preview.weml http://www.brainpop.com/math/geometryandmeasur ement/polygons/preview.weml http://www.brainpop.com/math/geometryandmeasur ement/polyhedrons/preview.weml http://www.brainpop.com/math/geometryandmeasur ement/polyhedrons/preview.weml http://www.brainpop.com/math/geometryandmeasur ement/typesoftriangles/preview.weml http://www.brainpop.com/math/geometryandmeasur ement/typesoftriangles/preview.weml

16. 4.1 Exploring Nets http://www.youtube.com/watch?v=y0IDttN W1Wo&feature=related

17. A Prism A prism has 2 congruent bases and is named for its bases. When all its faces, other than the bases, are rectangles and they are perpendicular to the bases, the prism is a right prism. A regular prism has regular polygons as bases.

18. Which one is a Right Prism?

19. Pyramid A regular pyramid has a regular polygon as its base. Its other faces are triangles. They are named after its base.

20. Describe the faces of: A Cube 6 congruent squares A Right Square Pyramid 1 square, 4 congruent isosceles triangles A Right Pentagonal Prism 2 regular pentagons, 5 congruent rectangles

21. Nets A net is a diagram that can be folded to make an object. A net shows all the faces of an object http://www.senteacher.org/wk/3dshape.php

22. Nets A net is a two-dimensional shape that, when folded, encloses a three-dimensional object. http://www.youtube.com/watch?v=9KXuaT18Jyw&feature=rel ated (quick) http://www.youtube.com/watch?v=9KXuaT18Jyw&feature=rel ated http://www.youtube.com/watch?v=9KXuaT18Jyw&feature=rel ated The same 3-D object can be created by folding different nets. You can draw a net for an object by visualizing what it would look like if you cut along the edges and flattened it out. http://www.youtube.com/watch?v=rMNa9wICWbo&feature=relate d http://www.youtube.com/watch?v=rMNa9wICWbo&feature=relate d

23. 4.2 Creating Objects From Nets

25. Turn to p. 178 of Textbook This diagram is not a rectangular prism! Here is the net being put together

26. p. 178 of Textbook Example #1a 2 congruent regular pentagons 5 congruent rectangles

27. p. 178 of Textbook Example #1b 1 square 4 congruent isosceles triangles

28. p. 178 of Textbook Example #1c This net has 2 congruent equilateral triangles and 3 congruent rectangles. The diagram is a net of a right triangular prism. It has equilateral triangular bases.

29. p. 178 of Textbook Example #1d This is not a net. The two triangular faces will overlap when folded, and the opposite face is missing. Move one triangular face from the top right to the top left. It will now make a net of an octagonal pyramid.

30. p. 179 of Textbook Example #2

31. 4.3 Surface Area of a Right Rectangular Prism

32. What is Surface Area? Surface area is the number of square units needed to cover a 3D object It is the sum of the areas of all the faces of an object

33. Finding SA of a Rectangular Prism The SA of a rectangular prism is the sum of the areas of its rectangular faces. To determine the surface area of a rectangular prism, identify each side with a letter. Rectangle A has an area of A = l x w A = 4 x 5 A = 20 Rectangle B has an area of A = l x w A = 7 x 5 A = 35 Rectangle C has an area of A = l x w A = 7 x 4 A = 28 A B C

34. Finding SA of a Rectangular Prism To calculate surface area we will need 2 of each side and add them together SA = 2(A) + 2(B) + 2(C) SA = 2(l x w) + 2(l x w) + 2(l x w) SA= 2(4 x 5) + 2(7 x 5) + 2(4 x 7) SA = 2(20) + 2(35) + 2(28) SA = 40 + 70 + 56 SA = 166 in 2 A B C

35. Finding SA of a Rectangular Prism Another Example SA = 2(A) + 2(B) + 2(C) SA = 2(l x w) + 2(l x w) + 2(l x w) SA= 2(8 x 10) + 2(7 x 8) + 2(10 x 7) SA = 2(80) + 2(56) + 2(70) SA = 160 + 112 + 140 SA = 412 units 2 A B C

36. Finding SA of a Rectangular Prism You Try SA = 2(A) + 2(B) + 2(C) SA = 2 (l x w) + 2(l x w) + 2 (l x w) SA= 2(15 x 6) + 2(10 x 6) + 2(10 x 15) SA = 2(90) + 2(60) + 2(150) SA = 180 + 120 + 300 SA = 600 cm 2 A B C

37. Some Video Reminders http://www.youtube.com/watch?v=oR1ukNC1pv A http://www.youtube.com/watch?v=oR1ukNC1pv A http://www.youtube.com/watch?v=agIV623B3nc &feature=related http://www.youtube.com/watch?v=agIV623B3nc &feature=related

38. Practice Pg p.186 #4, 6,7,10,12,13,15

39. 4.4 Surface Area of a Right Triangular Prism

40. Surface area of a Right Triangular Prism To calculate the surface area of right triangular prism, draw out the net and calculate the surface area of each face and add them together.

41. Surface area of a Right Triangular Prism Draw and label the net 12cm 20cm 16cm 10cm 20cm A B C D D

42. Surface area of a Right Triangular Prism SA = A area + B area + C area + 2 D area SA = A(l x w) + B(l x w) + C(l x w) + 2 * D[(b x h) ∕ 2)] SA = A(16 x 10) + B(10 x 12) + C(20 x 10) + 2 * D[(16 x 12) ∕ 2] SA = 160 + 120 + 200 + (2 * 96) SA = 160 + 120 + 200 + 192 SA = 672 cm 2 12cm 20cm 16cm 10cm 20cm A B C D D

43. Surface area of a Right Triangular Prism Draw and label the net 8cm 10cm 6cm 15cm 10cm A B C D D

44. Surface area of a Right Triangular Prism SA = A area + B area + C area + 2 D area SA = A(l x w) + B(l x w) + C(l x w) + 2 * D[(b x h) ∕ 2)] SA = A(15 x 6) + B(15 x 8) + C(15 x 10) + 2 * D[(6 x 8) ∕ 2] SA = 90 + 120 + 150 + (2 * 18) SA = 90 + 120 + 150 + 36 SA = 396 cm 2 8cm 10cm 6cm 15cm 10cm A B C D D

45. Surface area of a Right Triangular Prism Draw and label the net 2.3m 2.7m 1.4m 0.7m 2.7m A B C D D

46. Surface area of a Right Triangular Prism SA = A area + B area + C area + 2 D area SA = (l a x w a ) + (l b x w b ) + (l c x w c ) + 2[(l d x w d ) ∕ 2)] SA = (1.4 x 0.7) + (0.7 x 2.3) + (2.7 x 0.7) + 2 [(1.4 x 2.7) ∕ 2] SA = 0.98 + 1.61 + 1.89 + 2(1.89) SA = 8.26m 2 2.3m 2.7m 1.4m 0.7m 2.7m A B C D D

47. Surface area of a Right Triangular Prism Draw and label the net 8cm ? m 3m 3cm 3m 7 m ?m A B C D D 7 m

48. Surface area of a Right Triangular Prism Before you can solve, you need to find the missing side using Pythagorean Theorem! 8cm ? m 3m 3cm 3m 7 m ?m A B C D D

49. Surface area of a Right Triangular Prism 8m ?m 3m 7 m 8.54m

50. Surface area of a Right Triangular Prism SA = A area + B area + C area + 2 D area SA = A(l x w) + B(l x w) + C(l x w) + 2 * D[(l x w) ∕ 2)] SA = A(3 x 7) + B(7 x 8) + C(8.54 x 7) + 2 * D[(3 x 8) ∕ 2] SA = 21 + 56 + 59.78 + (2 * 12) SA = 21 + 56 + 59.78 + 24 SA = 160.78 m 2 8m ?m 3m 7 m 8.54m A BC D D

51. Some Review Videos http://www.youtube.com/watch?v=9pQknZ9fRTA http://www.youtube.com/watch?v=mL7E_NBhyI w&feature=related http://www.youtube.com/watch?v=mL7E_NBhyI w&feature=related

52. Practice P. 191

53. 4.5 Volume of a Right Rectangular Prism

54. Videos VIDEO Volume of a right rectangle http://www.youtube.com/watch?v=HYyBP4K65TI

55. The Formula V = Ah Volume equals the area of the base of the rectangle times its height – this applies to all right cylinders or prisms http://www.youtube.com/watch?v=QR22Zvpj3L4 &feature=relmfu http://www.youtube.com/watch?v=QR22Zvpj3L4 &feature=relmfu

56. Example 1 V = Ah V = (l x w) x h V = (13.5 x 5) x 18.5 V = 67.5 x 18.5 (not really needed) V = 1248.75 cm 3

57. Example 2 Jack’s family opened a full carton of frozen yogurt for dessert. After they ate, there was ¾ left. Jack wants to know what volume of frozen yogurt they ate. He measured the carton to be to have a length of 12cm, a width or 9 cm and a height of 18cm. V = Ah V = (l x w) x h V = (12 x 9) x 18 V = 1944 cm 3 (Volume of entire container – we want ¾ of the container ) V = 1944 x ¾ V = 1458 cm 3

58. Workbook Read “Quick Review” on pg. 85 Complete pg 85-86

59. 4.6 Volume of a Right Triangular Prism

60. Video Clip Relationship of a right triangular prism with right rectangular prism http://www.youtube.com/watch?v=NqlyyVrHnp8

61. Formula Volume is equal to the area of the base of the triangle times the length Volume is equal to the area of the base of the triangle times the length V = Al

62. Example 1 V = Al V = (b * h /2) x l V = (3 x 8 /2) x 7 V = (24 /2) x 7 V = 12 x 7 V = 84 m 3

63. Example 2 A glass vase in the shape of a right triangular prism is filled with coloured sand as a decoration. What is the volume of the vase. It measured 15cm by 8cm by 80cm V = Al V = (b * h /2) x l V = (15 x 8 /2) x 80 V = 60 x 80 V = 4800 cm 3

64. Watch Brainpop: Volume of Prisms http://www.brainpop.com/math/geometryandme asurement/volumeofprisms/preview.weml http://www.brainpop.com/math/geometryandme asurement/volumeofprisms/preview.weml

65. Workbook Complete pg. 87 - 89

66. 4.7 Surface Area of a Right Cylinder

67. Formula http://www.youtube.com/watch?v=GpHhvuRbB-8

68. Imagine a can. If you unwrap the label off the can, the lateral surface, or label, would be a rectangle. The height of the label is the same height as the can. The length of the label is the diameter of the base of the can because the label wraps all the way around the can.

69. Notes To find the surface area of a cylinder – sketch the net Remember that the width of the rectangle will be equal to the circumference of the circle (2πr) SA = 2(area of a circle) + area of the rectangle

70. Example 1 SA = 2πr 2 + (2πr)(h) SA = 2π(3.1) 2 + (2π(3.1))(12) SA = 2π(9.61) + (2π(3.1))(12) SA = 120.762822 + 230.734493 SA = 354.50inches 2

71. Example 2 SA = 2πr 2 + (2πr)(h) SA = 2π(9) 2 + (2π(9))(11) SA = 2π(81) + (2π(9))(11) SA = 508.938010 + 622.035345 SA = 1130.97m 2 9m 11m

72. Example 3 Calculate the outside surface area of the cylinder. The cylinder is open on one end. SA = πr 2 + (2πr)(h) SA = π(3) 2 + (2π(3))(11) SA = π(9) + (2π(3))(11) SA = 28.274333 + 207.345115 SA = 235.62m 2 3m 8m

73. Review Video http://www.youtube.com/watch?v=5GODwuQxY No&feature=related http://www.youtube.com/watch?v=5GODwuQxY No&feature=related

74. Workbook Complete pg 90 - 92

75. 4.8 Volume of a Right Cylinder

76. The Formula Cylinders follow the same properties as prisms for volume V = area of the base x height V = πr 2 x h

77. Example 1 V = πr 2 x h V = π(2 2 ) x 6 V = π(4) x 6 V = 12.6 x 6 V = 75.6 m 3 6m 2m

78. Example 2 Martha has a choice of two different popcorn containers at a movie. Both containers are the same price. Which container should Martha buy is she wants more popcorn for her money. Container 1: has a diameter of 20cm and height of 40cm. Container 2 has a diameter of 30cm and a height of 20cm.

79. Container 1 Radius is half the diameter so r = 10cm V = πr 2 x h V = π(10 2 ) x 40 V = π(100) x 40 V = 314.2 x 40 V = 12568 cm 3 Container 2 Radius is half the diameter so r = 15cm V = πr 2 x h V = π(15 2 ) x 20 V = π(225) x 20 V = 706.9 x 20 V = 14138 cm 3

80. Watch Brainpop: Volume of Cylinders http://www.brainpop.com/math/geometryandme asurement/volumeofcylinders/preview.weml http://www.brainpop.com/math/geometryandme asurement/volumeofcylinders/preview.weml

81. Workbook Complete pg 93 - 94