Measurement Unit. This booklet belongs to:

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1 Measurement Unit This booklet belongs to: LESSON # DATE QUESTIONS FROM NOTES Questions to review This booklet is homework and will be collected on the test day. Your teacher has important instructions for you to write down below. Write down the formulas you used to solve each question. (Show calculations.) Use. Round your answers to one decimal place, where necessary. What mark did you get on the practice test? /20 Did you do all your corrections? 1

2 Surface Area IRP # Daily Topic Key Ideas A6 determine an approximate square root of positive rational numbers that are non-perfect squares (This is a continuation of the learning targets from Rational numbers and square roots) A4 explain and apply the order of operations, including exponents, with and without technology. (This is a continuation of the learning targets from Rational numbers and square roots.) 1. Area Review: Rectangles, Circles & Triangles.Pg(4-7) Determine an approximate square root of a given rational number that is not a perfect square using technology (e.g., calculator, computer) Explain why the square root of a given rational number as shown on a calculator may be an approximation 2. Area Review: Rectangles, Circles & Triangles. (8-12) Solve a given problem by applying the order of operations with the use of technology 3. Surface Area Review: Prisms & Cylinders (Pg13-17) Solve a given problem by applying the order of operations with the use of technology Estimate the side length of a square with an area of 51cm 2 to the nearest tenth. Is your calculator answer, an exact answer? Explain Determine the area of rectangles, triangles & circles. Given, calculate the circumference of a circle with area 40cm 2. Determine the surface area of an isosceles triangular prism with the following dimensions; base 12cm, height 8 cm and width 3 cm. C2 determine the surface area of composite 3-D objects to solve problems [C, CN, PS, R, V] 4. Composite Shapes and Overlap(pg ) Determine the area of overlap in a given concrete composite 3-D object, and explain its effect on determining the surface area (limited to right cylinders, right rectangular prisms, and right triangular prisms) 5. Solve Problems Involving Surface Area (pg ) Determine the surface area of a given concrete composite 3-D object (limited to right cylinders, right rectangular prisms, and right triangular prisms) Solve a given problem involving surface area The two cylinders have respective radii of 5cm and 3 cm and surface areas of 200cm 2 and 100cm 2. Sandy glues the two cylinders together and paints the composite shape. How much must be subtracted from 300cm 2 to determine the new surface area? A painter is going to paint every surface except the base. How many surfaces need to be painted? Determine the total surface area Chapter Review and Practice Test Help students develop sound study habits. Many students will graduate high school saying they do not know how to study for math tests. Go over Practice Test Unit Evaluation 2

3 Important Terms and Formulas Area: Area: Area: or Cylinder Surface Area: Rectangular Prism Surface Area: Triangular Prism Surface Area: Pythagorean Theorem: For any right triangle. A net of an object. The net of a rectangular prism is given below. 3

4 AREA: Circles, Rectangles and Triangles. Review the markings and measurements for each shape. or Measurement Notes: Determine the area of each shape. Show calculations. Use. 1. Determine the area a two by eight rectangle. 2. Determine the area of a square with side length 2.4cm 3. Determine the area. 4. Determine the area. 5. Determine the area. 6. Determine the area of a circle with radius 7m after a circle with radius 3m has been cut out. 4

5 Square Roots, Pythagoras and Calculators Challenge #1: 7. Estimate the side length of a square with an area of 51cm 2 to the nearest tenth. Write down the steps to solve the challenge to the left. Confirm your answer with a calculator. Is your calculator answer, an exact answer? Explain Challenge #2: 8. Determine the area of a right triangle with a hypotenuse of length 10cm and one side of length 6cm. Write down the steps to solve the challenge to the left. Challenge #3: 9. The area of a right triangle is 40cm 2. One of the side lengths is 5cm. Find the other two sides. Round your answer to 1 decimal place. Write down the steps to solve the challenge to the left. 5

6 Using square roots and technology to solve problems. 10. Determine the side length of a square with an area of 25cm Determine the side length of a square with an area of 36cm Estimate the side length of a square with an area of 31cm 2 to the nearest tenth. Confirm your answer with a calculator. 13. Estimate the side length of a square with an area of 51cm 2 to the nearest tenth. 14. Estimate the side length of a square with an area of 90cm 2 to the nearest tenth. 15. Estimate the side length of a square with an area of 20cm 2 to the nearest tenth. Confirm your answer with a calculator. Confirm your answer with a calculator. Confirm your answer with a calculator. 16. Determine the area of a right triangle with a hypotenuse of length 10cm and one side of length 6cm. 17. Determine the area of a right triangle with a hypotenuse of length 13cm and one side of length 12cm. 18. Determine the area of a right triangle with a hypotenuse of length 25cm and one side of length 7cm. 6

7 19. Determine the area of a right triangle with a hypotenuse of length 12cm and one side of length 9cm. Round your answer to one decimal place. 20. Determine the area of a right triangle with a hypotenuse of length 20cm and one side of length 15cm. Round your answer to one decimal place. 21. Determine the area of a right triangle with a hypotenuse of length 89cm and one side of length 39cm. Round your answer to one decimal place. 22. The area of a right triangle is 40cm 2. One of the side lengths is 5cm and is not the hypotenuse. Find the other two sides. Round your answer to 1 decimal place. 23. The area of a right triangle is 100cm 2. One of the side lengths is 10cm and is not the hypotenuse. Find the other two sides. Round your answer to 1 decimal place. 24. The area of a right triangle is 68cm 2. One of the side lengths is 4cm and is not the hypotenuse. Find the other two sides. Round your answer to 1 decimal place. 25. The area of a right triangle is 180cm 2. One of the side lengths is 16cm. Find the other two sides. Round your answer to 1 decimal place. 26. The area of a right triangle is 90cm 2. One of the side lengths is 8cm. Find the other two sides. Round your answer to 1 decimal place. 27. The area of a right triangle is 140cm 2. One of the side lengths is 15cm. Find the other two sides. Round your answer to 1 decimal place. 7

8 Challenge #4: 28. Determine the area of the isosceles triangle with side lengths 8mm, 10mm, 10mm. 29. Determine the area. Determine the area of each shape to one decimal place. Show calculations. Use. 30. Determine the area. 31. Determine the area. 32. Determine the area. 33. Determine the area. 34. Determine the area. 35. Determine the area. 8

9 Determine the area of each shape. Show calculations. 36. Determine the area. 37. Determine the area. 38. The length is twice the width. Determine the length and width if the area is 44mm Determine the area. 40. Determine the area. 41. Determine the area. 42. The area of a circle is 314cm 2. Determine the radius of the circle. 43. The area of a circle is 62.8cm 2. Determine the diameter of the circle. 44. Given, calculate the circumference of a circle with area 40cm 2. 9

10 Wanisha hires Living Stones Paving Stones do tile a patio for her in her back yard. The tiles are large square tiles measuring 0.6 metres. The pavers have given an approximate cost of $27 per tile including installation. 45. How much would it cost to buy the tiles to pave a square patio with surface area 9 m How much would it cost to buy the tiles to pave a square patio with surface area 8 m If the price was the same for both designs, which option do you think the Pavers would rather do? Why? 48. Wanisha does not want to spend more than $1000. She asks Living Stones Pavers, what the largest surface area they can tile for that price. Draw a picture that shows the biggest surface area using all of the tiles. Ensure that you neat. Show all measurements and calculations so that that Wanisha can understand your math. 10

11 SURFACE AREA People often use formulas and have no idea where they came from. Formulas are efficient and were written down to save people time. Can you figure a formula for each of the following 3-D shapes? Challenge #5: 49. Determine the surface area if l=5m, w=3m and h=10m. Write a formula that could be used to find the surface area of any rectangular prism. Challenge #6: 50. Determine the surface area if C=5m, w=2m, h=3m and b=4m. Write a formula that could be used to find the surface area of any triangular prism. Challenge #7: 51. Determine the surface area if r=5m and h=8m. Write a formula that could be used to find the surface area of any cylinder. 11

12 Surface Area Formulas Label each drawing accurately. 52. Rectangular Prism: 53. Right Triangular Prism: 54. Cylinder:, Label the prism based on the given formula. Label the prism based on the given formula. Label the prism based on the given formula. Draw a net. A net is a drawing that shows all surfaces of 3d object. 55. Draw the net of the rectangular prism to explain the formula 56. Draw the net of the triangular prism to explain the formula:, 57. Draw the net of the cylinder to explain the formula: 12

13 Visualizing Unseen Surfaces Determine the number of surfaces of each of the following 3 dimensional objects. 58. Determine the number of surfaces. 59. Determine the number of surfaces. 60. Determine the number of surfaces. 61. Determine the number of surfaces. 62. Determine the number of surfaces. 63. Determine the number of surfaces. 64. Determine the number of surfaces. 65. Determine the number of surfaces. 66. Determine the number of surfaces. 67. Determine the number of surfaces. 68. Determine the number of surfaces. 69. Determine the number of surfaces. 70. Determine the number of surfaces. 71. Determine the number of surfaces. 72. Determine the number of surfaces. 13

14 Calculating Surface Area. Draw each figure, label it, write down an appropriate formula and determine the surface area. Use. Round your answer to one decimal. 73. Determine the surface area of a cube with side length 4 cm. 74. Determine the surface area of a cylinder with a height of 8 cm and a radius of 3 cm. 75. Determine the surface area of an isosceles triangular prism with height of 5 cm, base 8 cm and width 12 cm. 76. The edge length of a cube is 5 cm. Determine the surface area. 79. A rectangular prism has dimensions 4 cm, 3cm, and 10 cm. Determine the surface area. 82. The diameter of a cylinder is 10cm with a height of 20 cm. Determine the surface area. 77. If the dimensions are doubled, estimate the new surface area. 80. If the dimensions are doubled, estimate the new surface area. 83. If the dimensions are doubled, estimate the new surface area. 78. If the dimensions are doubled, calculate the new surface area. 81. If the dimensions are doubled, calculate the new surface area. 84. If the dimensions are doubled, calculate the new surface area. 14

15 Calculate the surface area of each of the following rectangular prisms. 85. Determine the surface area of a rectangular prism with the following dimensions; length 8 cm, height 2 cm and width 4 cm. 86. Determine the surface area of a rectangular prism with the following dimensions; length 2 cm, height 5 cm and width 7 cm. 87. Determine the surface area of a rectangular prism with the following dimensions; length 9 cm, height 5 cm and width 2 cm. 88. Determine the surface area of a cube with side length of 4cm. 89. Determine an expression to represent the surface area of the rectangular prism. 5 cm X cm 90. Determine an expression to represent the surface area of the rectangular prism. y cm X cm X cm 8 cm Challenge #8: 91. Determine the surface area of an isosceles triangular prism with the following dimensions; base 12cm, height 8 cm and width 3 cm. 15

16 Calculate the surface area. 92. Determine the surface area of a right triangular prism with the following dimensions; base 8cm, height 3 cm and width 2 cm. 93. Determine the surface area of a right triangular prism with the following dimensions; base 6cm, height 7 cm and width 3 cm. 94. Determine the surface area of a right isosceles triangular prism with the following dimensions; shortest sides 10cm and width 2 cm. 95. Determine the surface area of an isosceles triangular prism with the following dimensions; base 12cm, height 8 cm and width 3 cm. 96. Determine the surface area of an isosceles triangular prism with the following dimensions; base 8cm, height 6 cm and width 4 cm. 97. Determine the surface area of an equilateral triangular prism with side lengths 8cm and width 4 cm. SA: Two triangles: Bottom Rectangle: Side Rectangles: *Side length is found by using Pythagoras cm 2 16

17 Calculate the surface area. 98. Determine the surface area of the cylinder with radius 4 cm and height of 5 cm. 99. Determine the surface area of the cylinder with radius 8 cm and height of 6 cm Determine the surface area of the cylinder with diameter 4 cm and length of 10 cm Determine the surface area of the cylinder with diameter 8 cm and height of 6 cm Determine the surface area of the cylinder with diameter 8 cm and height of 6 cm without a lid Determine the outside surface area of the cylinder (not the inside), with radius 5 cm, height 4 cm without a lid or a bottom. Challenge #9: 104. Consider the surface area of a composite shape in terms of the basic 3d shapes it is made up of Consider the surface area of a composite shape in terms of the basic 2d shapes that cover it. Rectangular prism(s) Right triangular prism(s) Cylinder(s) Rectangle(s) Right triangle(s) Circle(s) 17

18 Composite Shapes and Overlap Consider the surface area of a composite shape in terms of the basic 3d shapes it is made up of How many of each basic shape make up the composite shape? 107. How many of each basic shape make up the composite shape? 108. How many of each basic shape make up the composite shape? Rectangular prism(s) Rectangular prism(s) Rectangular prism(s) Right triangular prism(s) Right triangular prism(s) Right triangular prism(s) Cylinder(s) Cylinder(s) Cylinder(s) Consider the surface area of a composite shape in terms of the basic 2d shapes that cover it How many of each basic shape make up the composite shape? 110. How many of each basic shape make up the composite shape? 111. How many of each basic shape make up the composite shape? Rectangle(s) Rectangle(s) Rectangle(s) Right triangle(s) Right triangle(s) Right triangle(s) Circle(s) Circle(s) Circle(s) Which of the above methods do you like better and why? 18

19 Consider the surface area of a composite shape in terms of the basic 3d shapes it is made up of How many of each basic shape make up the composite shape How many of each basic shape make up the composite shape How many of each basic shape make up the composite shape. Rectangular prism(s) Right triangular prism(s) Cylinder(s) Rectangular prism(s) Right triangular prism(s) Cylinder(s) Rectangular prism(s) Right triangular prism(s) Cylinder(s) Consider the surface area of a composite shape in terms of the basic 2d shapes that cover it How many of each basic shape make up the composite shape How many of each basic shape make up the composite shape How many of each basic shape make up the composite shape. Rectangle(s) Right triangle(s) Circle(s) Rectangle(s) Right triangle(s) Circle(s) Rectangle(s) Right triangle(s) Circle(s) Which of the above methods do you like better and why? 19

20 Draw a picture, spot the error in the solution and correct it. (Be specific) 118. Draw a rectangular prism with a rectangular prism cut through the center of it Draw a cylinder with a smaller cylinder cut through the middle of it. Solution: 1 st Calculate the surface area of the larger rectangular prism first. 2 nd Calculate the surface area of the smaller rectangular prism and subtract it from the bigger one. 3 rd Finished. Solution: 1 st Calculate the surface area of the larger cylinder first. 2 nd calculate the surface are of the top circles of the smaller cylinder and subtract it from the larger cylinder. 3 rd Finished Draw a cylinder with a rectangular prism cut through the center of it Draw a rectangular prism with a right triangular prism cut through the center of it. Solution: 1 st Calculate the surface area of the cylinder first. 2 nd Calculate the surface area of the 4 internal sides and add them to the area of the cylinder. 3 rd Finished. Solution: 1 st Calculate the surface area of the rectangular prism first. 2 nd Calculate the surface area of the 2 triangular holes ands subtract that from the rectangular prisms surface area. 3 rd Finished. 20

21 Describe the correct strategy Two cylinders below have respective radii of 10cm and 4 cm and surface areas of 400cm 2 and 226cm The two cylinders have respective radii of 5cm and 3 cm and surface areas of 200cm 2 and 100cm 2. Brady glues the two cylinders together and paints the composite shape. He reasons that the total surface area to be painted can be calculated by adding 400cm 2 and 226cm 2 for a total of 626cm 2. Sandy glues the two cylinders together and paints the composite shape. How much must be subtracted from 300cm 2 to determine the new surface area? What is the actual surface after of the composite shape? Draw a picture to help Brady understand Jenna s stategy to determine the total surface area is to calculate the surface area of each rectangular prism and then subtract the overlap. How much will she have to subtract? 125. Vangel s strategy to determine the total surface area of the composite shape is to calculate the surface of rectangular prism and add it to half the area of the cylinder. Will this work? If not, explain why and by how much will her measurement will be off. 21

22 Solve Problems Involving Surface Area Challenge #10: 126. Determine the total surface area excluding the base. How many surfaces need to be painted? Determine the total surface area. Joe Painter wants to buy the right amount of paint to cover each concrete structure once If he does not paint the bottom surface, How many surfaces need to be painted? Determine the total surface area If he does not paint the bottom surface, How many surfaces need to be painted? Determine the total surface area If he paints every surface, determine the total surface area to be covered. Solution: Large rectangles: Minus one circle: Side squares: Side of cylinder: Plus one circle: =214.8 cm 2 Remember that we don t need the bottom surface of the rectangle 22

23 Randal needs to paint the following composite shapes If he does not paint the bottom surface, How many surfaces need to be painted? Determine the total surface area If he paints every surface, determine the total surface area to be covered If he paints every surface, determine the total surface area to be covered Calculate the total surface area excluding the base Calculate the total surface area excluding the base Pro-painters forgot to paint the cylinders grey. Determine the total surface area still to be painted. 23

24 136. Calculate the total surface area excluding the base Calculate the total surface area Calculate the total surface area to paint the steps excluding the base and the left side that meets the house. 24

25 Review Check List Definitions: Pg # Face it * Go to page 3 and write down any definitions that you are unsure of. Define each word and be able to show your understanding with examples. 3 Learning Target Example Pg # Face it Determine an approximate square root of a given Estimate the side length of a square with an area of 5,6 rational number that is not a perfect square using 51cm 2 to the nearest tenth. technology (e.g., calculator, computer) (a6) Explain why the square root of a given rational number as shown on a calculator may be an approximation. (a6) Solve a given problem by applying the order of operations with the use of technology. (a4) Determine the area of overlap in a given concrete composite 3-D object, and explain its effect on determining the surface area (limited to right cylinders, right rectangular prisms, and right triangular prisms) Is your calculator answer, an exact answer? Explain 5,6 Given, calculate the circumference of a circle with area 40cm 2. The two cylinders have respective radii of 5cm and 3 cm and surface areas of 200cm 2 and 100cm 2. Sandy glues the two cylinders together and paints the composite shape. How much must be subtracted from 300cm 2 to determine the new surface area? 9 21 Determine the surface area of a given concrete composite 3-D object (limited to right cylinders, right rectangular prisms, and right triangular prisms) Solve a given problem involving surface area See page See page *Face it. When you have mastered the content draw a OR if you are unsure, draw a and ask for help. 25

26 Practice Test Score /27 Write this test and do not look at the answers until you have completed the entire test. Mark the test and decide whether or not you are happy with the result. FACE IT! Successful students will go back in the guidebook and review any questions they got wrong on this test. The following formulas may be of use for parts of the test. Rectangle A= lw Rectangular Prism SA = 2 (wh + lw + lh) Triangle A = bh/2 or A = ½bh Cylinder SA = 2πr 2 + 2πrh Circle A = πr 2, C = 2πr Right Triangular Prism SA = bh + ws + wh + wb Determine the area 1. Determine the area of a square with side length 6.2cm. 2. Determine the area a right triangle with side lengths 10cm, 8cm & 6cm. 3. Determine the area of a circle with a diameter of length 20cm. 4. Determine the side length of a square with an area of 61cm 2 to the nearest tenth. 5. The area of a triangle is 40cm 2. One of the side lengths is 8cm. Find the other two sides. Round your answer to 1 decimal place. 6. Determine the area of a circle with radius 10m after a circle with radius 5m has been cut out. Determine the number of faces on each shape

27 10. Label the rectangular prism with a length of 5cm, a width of 2cm and a height of 4 cm, draw its net, and calculate the surface area. 11. Label the triangular prism with a base of 10cm, a width of 5cm and a height of 8cm, draw its net and calculate the surface area. 12. Label the cylinder with a radius of 12cm and a height of 10cm, draw its net and calculate the surface area. A. Draw the net: A. Draw the net: A. Draw the net: B. Total surface Area. B. Total surface Area. B. Total surface Area. 13. Determine an expression to represent the surface area of the rectangular prism. 10 cm X cm 14. Determine the surface area of an isosceles triangular prism with the following dimensions; base 12cm, height 8 cm and width 3 cm. 15. Determine the outside surface area of the cylinder (not the inside), with radius 6 cm, height 5 cm without a lid or a bottom. X cm 27

28 16. Spot the error. Draw a cylinder with a smaller cylinder cut through the middle of it. Solution: 1 st Calculate the surface area of the larger cylinder first. 2 nd calculate the surface are of the inside cylinder and add it to the surface area of the larger cylinder. 3 rd Finished. 17. Spot the error. Vangel s strategy to determine the total surface area is as follows: Determine the total surface area of the rectangular prism and subtract over lapping rectangle from the surface area. Calculate the surface area of a cylinder, divide by two and then subtract the overlapping rectangle from the surface area. 18. Scott is building a green house out of glass for his tomato plants. Determine the total surface area of glass needed to complete this project if: The green house has square base of 64 square feet and a height The front rectangular panel has a height of 7 feet and the overall height of the green house is 10 feet. How much will Vangel s answer be off by? 19. Calculate the total surface area excluding the base. 20. Calculate the total surface area excluding the base. 28

29 Measurement Answer Key 1. 16m cm 2 (5.76) 3. 6cm m cm 2 (50.24) m 2 ( Should be closer to 7 than 8., Calculator: 7.1 ( ), No, the calculator rounded the last digit cm cm and 16.8cm (root 281) 10. 5cm 11. 6cm 12. A tiny bit closer to 6 than 5, Calculator: 5.6cm ( ) 13. Answers will vary should be closer to 7 than 8., Calculator: 7.1 ( ), 14. Slightly closer to 9 than 10., Calculator: 9.5cm ( ) 15. Slightly close to 4 than 5., Calculator: 4.5 ( ) cm cm cm cm cm cm cm, 16.8 cm cm, 22.4 cm cm and 34.2 cm cm and 27.6 cm cm, 23.9cm cm, 23.9cm cm cm cm mm cm cm cm cm cm cm , cm cm (16x+2)cm cm cm cm 45. $ Same price. Still have to use the same number of tiles m 2 because they would not have to make any cuts. It would be faster for them. 48. A 6 by 6 is the biggest. The SA would be m cm cm cm See web 53. See web 54. See web cm m cm cm SA 4 times 78. SA 4 times: 600cm cm SA 4 times 81. SA 4 times: 656cm cm SA 4 times bigger? cm cm cm cm cm (2x 2 +20x) cm xy+16x+16y cm cm cm cm cm cm 2 192cm cm 2 29

30 cm cm cm cm cm cm cm RP, 2 RTP R, 4 RT RP, 2RTP RP, 2RTP RTP R, 4RT R, 1RT R, 4T RP, 1 Half Cylinder RP, 1RTP RP, 2 RTP R, 1C R, 2RT R, 4RT :true, 2:False Subtract the front and back rectangles and add the 4 rectangular inner walls to the larger prism s area and 2: true, 3:False add the wall (2πrh) to the larger cylinder s area and 2 true, 3:False subtract the front and back surface rectangles from the larger surface area and 2 true, add the 3 internal rectangular sides to the larger surface area Actual is cm 2. He forgot to subtract the over lap.(two circles with radius 4cm.) cm 2 must be subtracted m 2 must be subtracted Her measurement will be 16 cm 2 to big. The rectangular prism has one side covered by the half cylinder. The cylinder does not have any overlap to be subtracted cm m cm cm cm cm cm m m cm cm cm cm 2 Practice Test cm cm cm cm cm m cm cm cm x 2 +40x cm cm cm and 2 are true. 3 is false. Still need to subtract the 2 circles that make the holes. 17. Vangel s answer will be 16 cm 2 too small. The cylinder does not add any overlap because the rectangle is in the middle of the cylinder ft m cm 2 30