Main Idea Convert Units Of Area And Volume

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Multi-Part Lesson9-1Convert MeasurementsPARTMain IdeaConvert units ofmeasure betweendimensions includingarea and volume.glencoe.comABCDEFConvert Units of Areaand VolumeCARPETING Jonathan is carpeting hisbedroom. It is 15 feet long and 12 feetwide. While shopping, he noticescarpet is sold in square yards.12 ft1. How many feet are in one yard? 32. How many yards long is the room? 515 ft3. How many yards wide is the room? 44. What is the area of the room in square yards? 20 yd2 " You can use the formula for the area of a square,A s2, to find thenumber of square feet in one square yard.Convert Area MeasurementsConvert one square yard to square feet.A square yard is a square with a side length of one yard. You knowthat one yard is equal to three feet. So, one square yard is a squarewith side length three feet.1 ydA s2Write the formula.A 32Replace s with 3.A 9Simplify.So, one square yard is equal to9 square feet.1 ft1 ft1 ft1 ft1 yd1 ft1 ftConvert one square meter to square centimeters.A square meter is a square with a side length of onemeter. YouC09-014A-891643know that one meter is equal to 100 centimeters. So, one squaremeter is a square with side length 100 centimeters.A s2Write the formula.A 1002Replace s with 100.A 10,000Simplify.So, one square meter is equal to 10,000 square centimeters.Lesson 9-1 Convert Measurements517 522 SE.indd 5175177/10/09 2:49:27 PM

Complete.a. 1 ft2 in2 144b. 1 cm2 mm2 100You can use the formula for the volume of a prism, V bwh, toconvert cubic units.Convert Volume MeasurementsFormulas Since a cubehas three equaldimensions, volume canalso be found with theformula V s 3, where s isthe length of a side.Convert one cubic foot to cubicinches.1 ft 12 in.A cubic foot is a cube with a sidelength of one foot or 12 inches.V bwh1 ft 12 in.Write the formula.V 12 · 12 · 12 Replace b, w, and h with 12.V 1,7281 ft 12 in.Simplify.So, one cubic foot is equal to 1,728 cubic inches.C09-015A-891643Complete.c. 1 yd3 ft3 27d. 1 cm3 mm3 1,000The table gives several common measurement conversions for squareunits and cubic units.Measurement ConversionsAreaVolumeCustomary Units1 ft2 144 in2Metric Unitscm211 yd2 9 ft21 cm2 100 mm21 ft3 1,728 in31 m3 1,000,000 cm31 yd3 27 ft31 cm3 1,000 mm3m2 10,000Each relationship in the Key Concept box can be written as a unitratio. To convert square or cubic units, use the unit ratio or itsreciprocal.518Chapter 9 Measurement and Proportional Reasoning517 522 SE.indd 5187/10/09 2:49:30 PM

Convert MeasurementsCONSTRUCTION A roof is 25 feet by 35 feet. How many squareyards is the roof? Round to the nearest tenth.Formulas The formula forfinding the area of arectangle is A b w.The area of the roof is 25 feet 35 feet or 875 square feet. Use the9 ftreciprocal of the unit ratioto find the number of square yards.221 yd1yd2875 ft2 875 ft2 ·29 ft1yd2 875 ft2 ·9 ft22875 yd or 97.2 yd291 yd29 ftMultiply by.2Divide out common units, leaving the desiredunit, yards.Divide.The roof is 97.2 square yards.e. CEREAL A cereal box holds 320 cubic inches of cereal. How manycubic feet is this? Round to the nearest tenth. 0.2 ft3The metric system also relates length, mass, and capacity.Length, Mass, and CapacityWords1 milliliter has the same volume as1 cubic centimeter.Symbols1 mL 1 cc1 milliliter of water is approximately 1 gram.1 mL 1 gConvert Volume to CapacityConvert one cubic meter to milliliters.A cubic meter is a cube with a side length of one meter or100 centimeters. Use 1 cc 1 mL to convert the rates.V b·w·hWrite the formula.V 100 · 100 · 100 Replace b, w, and h with 100.V 1,000,000Simplify.So, one cubic meter is equal to 1,000,000 milliliters.Complete.f. 17,000 mm3 mL 17g. 150 cc L 0.15Lesson 9-1 Convert Measurements517 522 SE.indd 5195197/10/09 2:49:32 PM

indicates multi-step problemExamples 1 and 2(p. 517)Complete.1. 3 ft2 in2 4322. 4 yd2 ft2 364. 3.2 m2 cm2 32,000 5. 900 mm2 cm2 9Examples 3 and 4(pp. 518–519)(p. 519)6. 8 cm2 mm2 800Complete.7. 0.2 ft3 in3 345.610. 5,600 mm3 mL5.6Example 53. 720 in2 ft2 58. 4,320 in3 ft3 2.511. 4.1 m3 cm34,100,00013. FENCING A playground issurrounded by chain-linkfencing. The dimensions ofthe playground are 52 feetby 37 feet. How many squareyards does the fencingsurround? Round to thenearest tenth if necessary. 213.8 yd29. 1.5 yd3 ft3 40.512. 2 cm3 mL 237 ft52 ft " 14. SCUBA DIVING Maria is using a cylindrical oxygen tank while scubadiving. It holds 80 cubic inches of air. How many cubic feet of air is sheusing? Round to the nearest hundredth if necessary. 0.05 ft3 Step-by-Step Solutions begin on page R1.Extra Practice begins on page EP2.Examples 1 and 2(p. 517)Complete. Round to the nearest hundredth if necessary. 19. 75,00015. 11.5 ft2 in2 1,656 16. 1,396.8 in2 ft2 9.7 17 216 ft2 yd2 2418. 14 yd2 ft2 12619. 7.5 m2 cm221. 5.4 cm2 mm2 540 22. 597 mm2 cm25.97Examples 3 and 4(pp. 518–519)28. 6.7529. 450,000Example 5(p. 519)20. 980 cm2 m2 0.1023. 1 mi2 ft227,878,400Complete. Round to the nearest hundredth if necessary. 26. 10,471.6824. 3 yd3 ft3 8125. 11,232 in3 ft3 6.5 26. 6.06 ft3 in327. 280.8 ft3 yd3 10.4 28. 6,750 mm3 cm329. 0.45 m3 mL30. 7.7 cm3 mm37,70032. 1 yd3 in346,65631. 973,000 mL m30.9733. SPORTS Including the end zones, a football field is 360 feet long by160 feet wide. What is the area of a football field in square yards? 6,400 yd234. GARDENING Tabitha has a small garden. If the garden has an area of1,512 square inches, what is the area of the garden in square feet? 10.5 ft235. APPLIANCES A refrigerator has 25.3 cubic feet of space. How many cubicyards is this? 0.94 yd3520Chapter 9 Measurement and Proportional Reasoning517 522 SE.indd 5207/10/09 2:49:34 PM

36. 65,961 ft336. PARADE A cartoon character was depicted as a balloon in a parade. Theballoon contained 2,443 cubic yards of air. How many cubic feet is this?37. MEDICINE A specific medicine states that a dose is 2 teaspoons. If ateaspoon is equal to 5 milliliters, how many cubic centimeters is thedose? 10 cc38. How many square yards are in one square mile? 3,097,600 yd239. One square yard is equal to how many square inches? 1,296 in240. BOXES Two boxes are shown.40a. 1.276a. What is the difference oftheir volume, in cubic feet?b. How many times greateris the volume of Box Athan Box B? 814 in.7 in.12 in.15 in.#PY "c. What conclusion can youdraw about the volume ofa prism after its dimensions are halved?40c. The volume isone eighth of itsoriginal volume.6 in.7.5 in.#PY #41 SWIMMING POOL The world’s largest swimming pool is located in Chileand has a volume of 250,000 cubic meters. How many cubic yards is this? " (Hint: 1 meter 1.1 yards) 332,750 yd342. DOSAGES A liquid allergy medication comes in a bottle containing4 fluid ounces. How many 5 cubic-centimeter doses are in the bottle?(Hint: 1 fl oz 29.5 mL) 23.6 dosesC 43. REASONING Alberto measured his bedroom for new carpet. The room is43. He would169 square feet. When he got to the carpet store, all of the prices werehave to dividegiven in square yards. Explain how he would convert his calculations169 square feet byto square yards to determine the cost.9 since there are3 feet in each yard44. CHALLENGE The Art Club is tiling a wall 8 feet tall by 10 feet long. Each tileand he wasis a 3-inch square and costs 0.59. What is the cost of tiling the wall? 755.20converting tosquare yards.45. FIND THE ERROR Seth is converting the volume of his shed from cubicfeet to cubic inches. Find his mistake and correct it.45. He should havemultiplied by thereciprocal;1 ft38,640 ft3 8,640 ft3 x14,929,920 in3.1,728 in38,640 ft3 31,728 in46. They are both acustomary unit buta mile is a linearmeasurement anda square mile is anarea measurement. 5 in346.Compare and contrast one mile with one square mile.Lesson 9-1 Convert Measurements517 522 SE.indd 5215217/10/09 2:49:38 PM

Practice47. Which of the following measurements isNOT equivalent to the other three? B49.EXTENDED RESPONSE A freightcontainer has the dimensionsshown below.A. 400,000,000 cm2B. 4,000 m2C. 0.04 km2D. 40,000,000,000 mm248.8 ftGRIDDED RESPONSE Two studentswere asked to design a dog run with anarea of 36 feet. The first student made a9-foot-long by 4-foot-long run. Thesecond student made a square run thatwas 6 feet on each side. How manymore feet of fence will the first studentneed than the second? 22 ft8 ftPart A What is the volume of thecontainer in cubic feet? 128 ft3Part B " What is the volume of thecontainer in cubic inches? 221,184 in3Part C What is the volume of thecontainer in cubic meters? Round to thenearest tenth if necessary. 3.5 m3Complete. Round to the nearest tenth if necessary.50. 24 mi/h ft/s 35.2(Lesson 9-1E)51. 39 kg/min g/s 65052. 8.3 m/h yd/min 0.253. WEIGHTLIFTING A barbell weighs 10 pounds. What is its mass in kilograms?(Lesson 9-1D) 4.5 kg54. STORAGE The jar shown is used to store marinara sauce. What is thevolume of marinara sauce that can be stored? (Lesson 8-1C) 31.8 in31.5 in.55. FISHERY The table shows the population of various fish kept ata fishery. (Lesson 6-3B)4.5 in.Fishery PopulationFishMonth 1Month 2Herring2,3002,250Cod1,2501,450Flounder4,9004,725 " a. What was the percent of increase of cod from Month 1 to Month 2? 16%b. What was the percent of change of herring from Month 1 to Month 2? -2%c. Which fish had the greatest percent of change? cod522Chapter 9 Measurement and Proportional Reasoning517 522 SE.indd 5227/10/09 2:49:41 PM

518 Chapter 9 Measurement and Proportional Reasoning Complete. a. 1 ft2 in2 2144 2b. 1 cm mm 100 You can use the formula for the volume of a prism, V bwh, to convert cubic units. Convert Volume Measurements Convert one cubic foot to cubic inches. A cubic foot is a cube with a

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