Math 2201 Chapter 8 Review

Transcription

1 Olga Math 2201 Chapter 8 Review Multiple Choice 1. A 2 L carton of milk costs $3.26. What is the unit rate? a. $0.83/500 ml b. $3.27/2 L c. $0.61/L d. $1.63/L 2.. drove 346 km and used up 28.7 L of gas. What is her car's fuel efficiency? a L/100 km b. 12 ml/km c. 12 km/l d L/km 3. Maureen ran 15 km in 1.25 h. What is her running speed? a. 12 km/h b. 15 km/h c. 120 m/min d. 200 m/s 4. Which scale factor(s) will produce an image that is larger than the original? I II. 116% III. a. I only b. I and II only c. II and III only d. I, II, and III 5. Which scale factor(s) will produce an image that is smaller than the original? I. 37% II. III. 9.6 a. I only b. I and II only c. II and III only d. I, II, and III 6. A billboard is 5.0 m by 2.5 m. A scale diagram of the billboard must fit in a space that is 18 cm by 15 cm. Which scale would be the most reasonable one to use for the scale diagram?? a. 1 m:3 cm b. 30 cm:1 cm c. 1 cm:3 m d. 300% June

2 7. A computer chip is 12 mm by 26 mm. A scale diagram of the computer chip must fit in a space that is 40 cm by 70 cm. Which scale would be the most reasonable one to use for the scale diagram? a. 1 mm:33.3 cm b. 1 mm:26 cm c. 1 mm:3.3 cm d. 1 mm:2.6 cm 8. A photograph is 6 cm by 11 cm. A copy is made using a scale factor of 140%. What are the dimensions of the copy? a. 4.3 cm by 7.9 cm b. 8.4 cm by 15.4 cm c. 24 cm by 44 cm d. 43 mm by 79 cm 9. A photograph is 12 cm by 25 cm. A copy is made using a scale factor of 75%. What are the dimensions of the copy? a. 9 cm by 19 cm b. 90 cm by 19 cm c. 9 mm by 19 cm d. 9 m by 19 m 10. A room in a floor plan is 8.4 cm by 9.12 cm. The floor plan was made using a scale factor of What are the dimensions of the actual room? a. 2 m by 2.19 m b m by 21.9 m c. 3.5 m by 3.8 m d. 202 cm by 219 cm 11. The distance between two towns on a map is 16.5 cm. The map was made using a scale of 5 cm to 100 km. What is the actual distance between the two towns? a. 135 km b. 825 km c. 330 km d. 165 km 12. Which one of the following cylinders is similar to a cylinder that is 8 cm long and 2.5 cm in diameter? Choose the best answer. a. a cylinder 4 cm long and 1.5 cm in diameter b. a cylinder 12 cm long and 3.5 cm in diameter c. a cylinder 16 cm long and 5 cm in diameter d. all of the above 13. Which of the following boxes are similar to a gift box that is 10 cm by 8 cm by 16 cm? a. a box 20 cm by 19 cm by 30 cm b. a box 6 cm by 4 cm by 8 cm c. a box 15 cm by 13 cm by 21 cm d. none of the above June

3 a. Math 2201 Chapter 8 Review 14. A 1:25 scale model of a garbage truck is 0.5 ft tall, 0.32 ft wide, and 1.4 ft long. What are the dimensions of the actual garbage truck? a. 25 ft by 12.5 ft by 50 ft b. 9 ft by 6.4 ft by 25 ft c. 15 ft by 7.4 ft by 33.5 ft d ft by 8 ft by 35 ft 15. Cylinder A has a radius of 5 mm and a height of 30 mm. Cylinder B has a radius of 20 mm and a height of 120 mm. These two cylinders are similar. By what factor is the surface area of cylinder B greater than the surface area of cylinder A? a. 36 b. 4 c. 6 d A cylindrical oil tank is filled with 500 m3 of oil. A similar oil tank has dimensions that are reduced by a scale factor of What volume of oil will fill the smaller tank? a m 3 b. 148 m3 c. 333 m3 d. 222 m A cylindrical oil tank has a surface area of 1800 m2. A similar oil tank has dimensions that are reduced by a scale factor of. What is the surface area of the smaller tank? 800 m 2 b. 630 m2 c m2 d. 533 m2 Short Answer 18. Wayne and Steve work at a photocopy shop. They have an order to print and bind 500 copies of a business report. Steve finished 125 reports in 8.5 h and Wayne finished the remaining 375 reports in 22 h. Who worked at a faster rate? 19. On Wednesday a crew paved 12 km of road in 7 h. On Thursday, the crew paved 8 km in 6 h. On which day did they pave the road at the faster rate? 20. Giselle is deciding between two long-distance telephone plans: Plan A charges $15 per month, plus 2 /min. Plan B charges $10 per month, plus 6 /min. Giselle usually makes about 80 min of long distance calls each month. Which plan costs less? Show your calculations. 21. Moira loaned $300 to her roommate for 4 months and was paid back $310. What simple interest rate did she earn? 22. Determine the scale factor that was used to transform diagram X into diagram Y. Express your scale factor as a fraction and as a percent to one decimal place. June

4 23. On a plan, an actual length of 8.5 m is represented by 3 cm. Determine the scale and the scale factor of the plan. 24. The actual diameter of a loonie is 26 mm. In a scale diagram, the diameter of a loonie is 70.2 cm. What scale factor was used? 25. The actual width of a garage door is 3 m. In a scale diagram, the width of the garage door is 20 cm. What scale factor was used? Give your answer as a percent to one decimal place. 26. Leo has a microscope with a lens that magnifies by a factor of 80. He was able to capture the image of a slide containing human skin cells. In the image, the cell was about 5.6 mm long. Determine the length of the actual human skin cell, to nearest hundredth of a millimetre. 27. A standard music CD has an exterior diameter of 120 mm and an interior diameter of 15 mm. Draw a scale diagram of a CD using a scale factor of 60%. 28. A high school basketball court is 26 m by 15 m. Draw a rectangle to represent the outer boundary of a basketball court using a scale factor of Label the dimensions in centimetres. 30. The base and height of a triangle with an area of 80 cm 2 will be reduced by a scale factor of. Determine the area of the reduced triangle to two decimal places. 31. The scale factor for two similar rectangles is 1:5. The sum of their areas is 78 cm2. Determine the area of each rectangle. 32. The scale factor for two similar trapezoids is 1:3. The sum of their areas is 80 cm2. Determine the area of each trapezoid. 33. Triangle A has an area of cm2 and similar triangle B has an area of cm2. Determine what scale factor makes triangle B an enlargement of triangle A. 34. Rectangle A has an area of 12 cm2 and similar rectangle B has an area of 4.32 cm2. Determine what scale factor makes rectangle B a reduction of rectangle A. 35. Circle A has an area of 5 cm2 and similar circle B has an area of 45 cm2. Determine what scale factor makes circle B an enlargement of circle A. 36. The dimensions of a right hexagonal prism are enlarged by a scale factor of 6.5. Determine the value of. Do not round your answer. 37. The dimensions of a right hexagonal prism are enlarged by a scale factor of 6.5. Determine the value of. Do not round your answer. 38. The dimensions of a right hexagonal prism are enlarged by a scale factor of 6.5. Determine the value of. 39. An orange has a diameter of 8 cm. A honeydew melon has a diameter of 18 cm. Estimate how many times greater the volume of a melon is, compared with the volume of an orange. June

5 Problem 40. The floor plan for a small industrial company is drawn as shown, using a scale factor of a) What are the actual dimensions of the area for the office area and the storage areas? Show your work. b) What is the actual area, in square metres, of the work area? Show your work. 41. The floor plan for a greenhouse is shown below. The area of the actual floor is 300 m2. a) Determine the actual area that each square on the floor plan represents. b) Determine the actual distance that 5 mm on the floor plan represents. c) Determine the scale of the plan. d) Determine the scale factor that was used to draw the floor plan. 42. A band poster that measures 90 cm by 40 cm is reduced by a scale factor of so it can fit on a postcard. a) What are the dimensions of the postcard image? b) By what scale factor, to the nearest hundredth, was the area of the poster decreased in the reduction process? 43. A male moose is 2.6 m tall and 3.2 m long, with antlers that are 1.2 m across. An artist wants to carve scale models of the moose. She uses a scale factor of need to make 12 carvings?. What are the dimensions of the block of wood she would 44. A cook has a set of four mixing bowls with lids. The bowls stack inside each other and are similar to each other. The diameters of the two largest bowls are 30 cm and 26 cm. The scale factor is the same from each bowl to the next smaller bowl. The cook estimates that the largest bowl has a surface area of about 2100 cm2. Estimate the surface area of the smallest of the four bowls. MULTIPLE CHOICE 1. ANS: D 2. ANS: D 3. ANS: A 4. ANS: C 5. ANS: B 6. ANS: A 7. ANS: D 8. ANS: B 9. ANS: A 10. ANS: C 11. ANS: C 12. ANS: C 13. ANS: D 14. ANS: D 15. ANS: D 16. ANS: B 17. ANS: A June

6 SHORT ANSWER Math 2201 Chapter 8 Review Steve finished about 15 reports per hour. Wayne finished 17 reports per hour. Wayne worked at a faster rate. Wednesday: 1.7 km/h Thursday: 1.3 km/h They paved the road faster on Wednesday. The cost of Plan A for 80 min is: $ ($0.02) = $16.60 The cost of Plan B for 80 min is: $ ($0.06) = $14.80 Plan B costs less. 10% per year 22., 28.6% 23. scale: 3 cm:8.5 m or 3 cm:850 m scale factor: or about or 2700% 6.7% 0.07 mm The CD should have an exterior diameter of 72 mm and an interior diameter of 9 mm cm 2 3 cm2, 75 cm2 8 cm2, 72 cm e.g., about 11 times greater PROBLEM June

7 40. ANS: a) Divide each dimension on the scale diagram by to obtain the actual dimension. Office area: = 2500 cm or 25 m; = 500 cm or 5 m. The office area is 25 m by 5 m. Storage area #1: = 1500 cm or 15 m; = 1000 cm or 10 m. Storage area #2 has the same dimensions as storage area #1: 15 m by 10 m. b) e.g., Determine the area of the work area and the kitchen, which, on the scale drawing, has dimensions of 5 cm by 3 cm. Determine the actual dimensions of this area: = 2500 m or 25 m; = 1500 cm or 15 m. The actual area of the kitchen and work area is (25 m)(15 m) = 375 m 2. The actual dimensions of the kitchen are = 1000 cm or 10 m and = 500 cm or 5 m. Its actual area is (10 m)(5 m) = 50 m 2. Subtract the area of the kitchen. 375 m 2 50 m 2 = 325 m 2 The work area covers 325 m a) There are 48 squares on the floor plan. Each square represents 6.25 m2. b) Each unit square measures 5 mm by 5 mm. The area of each square is 2.5 m by 2.5 m or 6.25 m 2. Therefore, 5 mm represents 2.5 m on the diagram. c) The scale is 5 mm:2.5 m or 5 mm:2500 mm or 1:500. d) The scale factor is or ANS: a) Reduced dimensions = (scale factor)(original dimensions) Reduced length = (90 cm) Reduced length = 15 cm Reduced width = (40 cm) Reduced width = cm The postcard image is 15 cm by 6 cm. b) Area of similar shape = k 2 (Area of original shape) k 2 = k 2 = k 2 = The area of the poster was reduced by a scale factor of Multiply each dimension by the scale factor. model height = (2.6 m) model height = (260 cm) model height = 10 cm model length = (3.2 m) model length = (320 cm) model length = cm model width = (1.2 m) model width = (120 cm) model width = cm The model moose is about 10 cm by 12.3 cm by 4.6 cm. There are several ways to arrange the dimensions to get 12 carvings. e.g., Keep the height and length the same and multiple the width by 12: 12( cm) = cm Round values up so there is enough wood to make the models. The dimensions needed are 10 cm by 12.5 cm by 56 cm. June

8 44. The scale factor, k, from one bowl to another is. For surface area, use the square of the scale factor. Surface area of bowl = k2(surface area of next larger bowl) Surface area of first bowl = 2100 cm2 Surface area of second bowl = (2100 cm 2 ) Surface area of second bowl = cm 2 Surface area of third bowl = ( cm 2 ) Surface area of third bowl = cm 2 Surface area of fourth bowl = ( cm 2 ) Surface area of fourth bowl = cm 2 The surface area of the smallest bowl is about 890 cm 2. June