5-8 Scale Drawings and Models
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1 1. The model of a car is shown below. The actual car is 1 in. = 2 ft feet long. What is the scale of the model car? 2. On the map, the scale is 1 inch = 20 miles. What is the actual distance between Kansas City and St. Louis? 5. An area rug is 9 feet wide. In a photograph, the image of the rug is 3 inches wide. What is the scale? 1 in. = 3 ft 6. A large American flag measures 255 feet wide. In an advertisement for renting this flag, the image of the flag is 4 inches wide. What is the scale of the flag? 1 in. = ft 7. A floor plan is shown for the first floor of a new house. If one inch represents 24 feet, what are the actual dimensions of each of the rooms listed? 260 mi 3. Marco is designing a flower garden in his backyard that is 12 feet long and 10 feet wide. Make a scale drawing of the garden. Use a scale of 0.5 in. = 2 ft. Use -inch grid paper. a. living room b. deck c. kitchen a. 15 ft by 18 ft b. 30 ft by 9 ft c. 9 ft by 18 ft 4. A model airplane is built with a wing span of 23 inches. The actual wing span is 92 feet. What is the scale of the model? 1 in. = 4 ft esolutions Manual - Powered by Cognero Page 1
2 8. The actual measurements for rooms are given. Using the floor plan and scale below, find the measurements on the floor plan. a. master bedroom: 12 feet by 15 feet b. den: 18 feet by 9 feet c. dining room: 12 feet by 9 feet a in. by in. 10. The actual Mount Rushmore carving was made from a scale model with a scale of 1 in. = 1 ft. On the model, Teddy Roosevelt s moustache was 1 foot 8 inches long. a. Find the length of Roosevelt s moustache on the monument. b. What is the scale factor? c. If George Washington s face is 60 feet tall on the monument, how tall was his face on the model? a. 20 ft b. c. 60 in. or 5 ft Find the scale factor for each scale cm = 5 m b. in. by in. c. in. by in. 9. A skatepark is 24 yards wide by 48 yards long. Make a scale drawing of the skatepark that has a scale of in. = 10 ft inch = 8 yards in. = 3 ft ft = 15 yd cm = 2.5 mm esolutions Manual - Powered by Cognero Page 2
3 16. 8 in. = 200 mi 17. The 8 planets distance from the Sun is shown. 19. Model with Mathematics Find a small rectangular item you use on a daily basis. Make a scale drawing of that item. Then write a problem based on your scale drawing. See students work. 20. Persevere with Problems Rectangle ABCD is reduced by a scale factor new rectangle?. What is the area of the a. What scale would you use to create a scale drawing? b. Use centimeter grid paper and your scale from part a to create a map of the four planets closest to the Sun. a. Sample answer: in. = mi b. Sample drawing: 12 in Reason Inductively Determine whether the following statement is always, sometimes, or never true. Justify your reasoning. If the scale factor of a scale drawing is greater than one, the scale drawing is larger than the actual object. Always; sample answer: A scale factor of means that 3 units of the drawing is equal to 1 unit of the object, so the scale drawing or model will be larger than the actual object. 22. Which One Doesn't Belong? Identify the scale that does not have the same scale factor. Explain your reasoning. 18. You build a model with a scale of 1:25. Your friend builds a model of the same object with a scale of 1:50. Which model is bigger? Explain. your model; Sample answer: 10 cm = 10 m; Sample answer: All of the other scales have a scale factor of a scale factor of.. 10 cm = 10 m has esolutions Manual - Powered by Cognero Page 3
4 23. Persevere with Problems A model of an insect has a scale of 0.25 centimeter = 1 millimeter. Is the model smaller or larger than the actual insect? Justify your reasoning by using the scale factor. Sample answer: The model is larger than the actual insect. The scale factor is which means the model is 2.5 times as large as the insect. 24. Building on the Essential Question Compare and contrast scale and scale factor. Sample answer: The scale is the ratio of the length on the model with an actual length. The units of measure can be different. The scale factor is also a ratio, but the units of measure must be the same. 25. Desiree is drawing a model of the Washington Monument which has an actual height of feet. 26. Short Response A blueprint has a scale of 2 inches = 2 feet. What is the scale factor of the blueprint? 27. A scale drawing of a swimming pool is shown. What are the actual dimensions of the swimming pool? F 8 meters by 4 meters G 20 meters by 10 meters H 50 meters by 25 meters J 80 meters by 40 meters H What other information is needed to find the length of the model s sides on the square base? A the height of the top of the tower B the length of the actual base side C the age of the tower D the height of the tower s first story B 28. A map has a scale of 1.5 inches = 500 miles. How many inches on the map would represent 850 miles? Round to the nearest tenth. A 2.2 inches B 2.4 inches C 2.6 inches D 2.8 inches 29. C Solve each proportion. 4 esolutions Manual - Powered by Cognero Page 4
5 Write a list of the first ten terms in the numerical patterns described below. Pattern A Use the starting number 0 and the rule Add 4. Pattern B Use the starting number 0 and the rule Add 8. a. Compare the terms in pattern A to the terms in pattern B. How are they related? b. Explain why the two patterns are related as they are. Pattern A: 0, 4, 8, 12, 16, 20, 24, 28, 32, 36 Pattern B: 0, 8, 16, 24, 32, 40, 48, 56, 64, 72 a. Each term in pattern A is half its corresponding term in pattern B. b. Adding 4 is the same as adding half of Some species of bamboo can grow 245 inches in a week. Identify the constant of proportionality and then write an equation relating the height of the bamboo to the number of days. How much would a bamboo plant have grown after 3 days? 35; h = 35d ; 105 in. 37. The conversion factor for changing meters to feet is 1 meter 3.28 feet. Find the approximate distance in feet of the 110-meter dash. ; about ft Name the property shown by each statement (x + 4) = (x + 4) + 3 Commutative Property of Addition 39. (4y) 1 = 4y Multiplicative Identity Property 40. (6 4) 10 = 10 (6 4) Commutative Property of Multiplication = 0 Multiplicative Property of Zero (3x) = 3x Additive Identity 43. (5 2) 4 = 5 (2 4) Associative Property of Multiplication Simplify each expression (e + 2) 7 + e esolutions Manual - Powered by Cognero Page 5
6 45. (13 24) 0 0 esolutions Manual - Powered by Cognero Page 6
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