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5.4 Scale Drawings - Big Ideas Math

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English5.4SpanishScale DrawingsHow can you use a scale drawing to estimateSSTATESTANDARDSthe cost of painting a room?MA.7.A.1.61ACTIVITY: Making Scale DrawingsWork with a partner. You havhave decided that yourclassroom needs to be painted.paintStart by making ascale drawingg of each of the four walls. Measure each of the walls. Measure the locationslocation and dimensions ofparts that will nott be painted. Decide on a scale for your drawings. Make a scale drawindrawing of each of the walls.Sample: Wall #1Blue region needsto be painted.Scale: 1 cm : 1 ftChalk Board9 ftWall26 ft For each wall, find the area of the part that needs to be painted.DimensionsDimensions of the wall9 ft by 26 ft9 26 234 sq ftDimensions of the partthat will not be painted5 ft by 17 ft5 17 85 sq ftArea of painted part212Chapter 5AreaSimilarity and Transformations149 sq ft

EnglishSpanish2ACTIVITY:ACTIVITY: Usingi Scale DrawingsWork with a partner.You are using a paint that covers 200 square feetper gallon. Each wall will need two coats of paint.a. Find the total area of the walls from Activity 1that needs to be painted.b. Find the amount of paintyou need to buy.c. Estimate the total cost ofpainting your classroom.Interior latex paintRoller, pan, and brush set 40 per gallon 123. IN YOUR OWN WORDS How can you use a scale drawing to estimatethe cost of painting a room?4. Use a scale drawing to estimate the cost of painting another room,such as your bedroom or another room in your house.5. Look at some maps in your schoollibrary or on the Internet. Make a listof the different scales used on the maps.01234Miles6. When you view a map on the Internet,how does the scale change when youzoom out? How does the scale changewhen you zoom in?“I don’t get it. According tothis map, we only haveto drive 8 inches.”Use what you learned about scale drawings to completeExercises 4 – 7 on page 216.Section 5.4Scale Drawings213

English5.4SpanishLessonLesson TutorialsKey VocabularyScale Drawings and Modelsscale drawing, p. 214scale model, p. 214scale, p. 214scale factor, p. 215A scale drawing is a proportional two-dimensional drawing of an object.A scale model is a proportional three-dimensional model of an object.ScaleMeasurements in scale drawings and models are proportional tothe measurements of the actual object. The scale gives the ratiothat compares the measurements of the drawing or model withthe actual measurements.Study Tip1 in.10 miScales are writtenso that the drawingdistance comes first inthe ratio.drawing distance—1 in. : 10 miactual distancedrawingEXAMPLE1actualFinding an Actual DistanceWhat is the actual distance d between Miami and Key West?Pensacola10TallahasseeJacksonvillePanama CityStep 1: Use a centimeter rulerto find the distance onthe map between Miami and Key West.Gainesville95Daytona Beach75The map distance is about 2.5 centimeters.Step 2: Use the scale to write and solvea proportion.map distance1 cm2.5 cm— —50 mid miactual distance d 50 2.5Cross Products Propertyd 125Multiply.The distance between Miami and Key West isabout 125 miles.OrlandoTampaSarasota95Fort St. Lucie75FortLauderdaleNaplesMiamiKeyWest1 cm : 50 mi1. What is the actual distance between Pensacola and Jacksonville?Exercises 8–11214Chapter 5Similarity and Transformations

EnglishSpanish2EXAMPLEStandardized Test PracticeThe liquid outer core of Earth is 2300 kilometers thick. A scalemodel of the layers of Earth has a scale of 1 in. : 500 km. How thickis the liquid outer core of the model?A0.2 in. CrustLiquidoutercoreB 4.6 in. 1 in.500 kmC 0.2 km model thicknessx in.2300 km— —Solidinnercore1 in.500 km—D4.6 km actual thicknessx in.2300 km 2300 km —2300 km Multiply each side by 2300 km.4.6 xSimplify.The liquid outer core of the model is 4.6 inches thick. The correctB .answer is Mantle2. The mantle of Earth is 2900 kilometers thick. How thick is themantle of the model?A scale can be written without units when the units are the same. A scalewithout units is called a scale factor.EXAMPLE3Finding a Scale FactorA scale drawing of a spider is 5 centimeters long. The actual spider is10 millimeters long. (a) What is the scale of the drawing? (b) What isthe scale factor of the drawing?drawing lengthactual length5 cm10 mm1 cm2 mma. —— — —The scale is 1 cm : 2 mm.5 cmb. Write the scale with the same units.Use the fact that 1 cm 10 mm.1 cm2 mm10 mm2 mm51scale factor — — —The scale factor is 5 : 1.Exercises 12–163. A model has a scale of 1 mm : 20 cm. What is the scale factorof the model?Section 5.4Scale Drawings215

EnglishSpanishExercises5.4Help with Homework1. VOCABULARY Compare and contrast the terms scale and scale factor.2. CRITICAL THINKING The scale of a drawing is 2 cm : 1 mm. Is the scale drawinglarger or smaller than the actual object? Explain.3. REASONING How would you find a scale factor of a drawing that shows alength of 4 inches when the actual object is 8 feet long?6) 39 (- 3) 3 (- 9) 4 (- 1)9 (-Use the drawing and a centimeter ruler.4. What is the actual length of theflower garden?5. What are the actual dimensions ofthe rose bed?6. What are the actual perimeters of theperennial beds?perennial bedrose bedtulip bedperennialbed7. The area of the tulip bed is whatpercent of the area of the rose bed?1 cm : 5 ftUse the map in Example 1 to find theactual distance between the cities.18. Tallahassee and Gainesville9. Naples and Daytona Beach10. Fort Lauderdale and Panama City11. Tampa and JacksonvilleFind the missing dimension. Use the scale factor 1 : 12.Item2ModelActual3 12.MattressLength: 6.25 in.13.CorvetteLength:14.Water TowerDepth: 32 cmDepth:m15.WingspanWidth: 5.4 ftWidth:yd16.Football HelmetDiameter:Length:in.mmLength: 15 ftDiameter: 21 cm17. ERROR ANALYSIS A scale is 1 cm : 20 m. Describe andcorrect the error in finding the actual distance thatcorresponds to 5 cm.216Chapter 5Similarity and Transformationsin. 1 cm20 mxm5 cm— —x 0.25 m

EnglishSpanishUse a centimeter ruler to measure the segment shown. Find the scale of the drawing.120 m18.19.IrisCorneaPupilLens24 mmVitreoushumor20. REASONING You know the length and width of a scale model. What additionalinformation do you need to know to find the scale of the model?16 ft21. OPEN-ENDED You are in charge of creatinga billboard advertisement with thedimensions shown.a. Choose a product. Then design thebillboard using words and a picture.8 fttb. What is the scale factor of your design?YOUR AD HEREReduced drawing of blueprint22. BLUEPRINT In a blueprint, each square has a side length14of — inch.BedroomLivingrooma. Ceramic tile costs 5 per square foot. How muchwould it cost to tile the bathroom?b. Carpet costs 18 per square yard. How much wouldit cost to carpet the bedroom and living room?Bathroom1 in. : 16 ftc. Which has a higher unit cost, the tile or the carpet? Explain.23. REASONING You are making a scale model of the solar system. The radiusof Earth is 6378 kilometers. The radius of the Sun is 695,500 kilometers. Is itreasonable to choose a baseball as a model of Earth? Explain your reasoning.24.A map on the Internet has a scale of 1 in. : 10 mi. You zoom outone level. The map has been reduced so that 2.5 inches on the old map appearsas 1 inch on the new map. What is the scale of the new map?Plot and label the ordered pair in a coordinate plane.25. A( 4, 3)26. B(2, 6)SECTION 1.628. D( 3, 7)27. C(5, 1)29. MULTIPLE CHOICE A backpack is on sale for 15% off the original price. Theoriginal price is 68. What is the sale price?SECTION 4.3A 10.20 B 53 C 57.80 Section 5.4D 78.20 Scale Drawings217

the scale factor of the drawing? a. drawing length —— actual length 5 cm — 10 mm 1 cm — 2 mm The scale is 1 cm:2 mm. b. Write the scale with the same units. Use the fact that 1 cm 10 mm. scale factor 1 cm — 2 mm 10 mm — — 2 mm 5 1 The scale factor is 5:1. 3. A model has a scale of 1