measurement in two systems · 1.6 describe and explain a personal strategy used to determine a...
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BookletMark: 10 9 8 7 6 RE-Submit
MeasurementinTwoSystems
Thisbookletbelongsto:____________________________Period______
LESSON# DATE QUESTIONSFROMNOTES QuestionsthatIfinddifficult
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REVIEW
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Yourteacherhasimportantinstructionsforyoutowritedownbelow.
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MEASUREMENT TOPICS
Solveproblemsthatinvolvelinearmeasurementusing:
• SIandimperialunitsofmeasure.
• Estimationstrategies.• Measurementstrategies.
1.1Providereferentsforlinearmeasurement.
1.2CompareSIandImperialunitsofmeasure.
1.3Estimatealinearmeasureandexplaintheprocess.
1.4Justifythechoiceofunitsusedfordeterminingalinearmeasurement.
1.5Solveproblemsthatinvolvelinearmeasureusinginstrumentsavailable.
1.6Describeandexplainapersonalstrategyusedtodeterminealinearmeasurement.
ApplyproportionalreasoningtoproblemsthatinvolveconversionsbetweenSIandimperialmeasurement.
2.1UseproportionalreasoningtoconvertwithinorbetweenSIandImperialsystems.
2.2Solveaproblemthatrequiresconversionbetweenunits.
2.3Verifyusingunitanalysis,aconversionbetweenunits.
2.4Justify,usingmentalmathematics,thereasonablenessofasolutiontoaconversionproblem.
Solveproblems,usingSIandimperialmeasurement,thatinvolvethesurfaceareaandvolumeof3-Dobjects,including
• Rightcones• Rightcylinders• Rightprisms• Rightpyramids• Spheres.
3.1Sketchadiagramtorepresentaproblemthatinvolvessurfaceareaorvolume.
3.2DeterminetheSAofarightcone,rightprism,rightpyramid,orsphereusinganobjectordiagram.
3.3DeterminetheVofarightcone,rightprism,rightpyramid,orsphereusinganobjectordiagram.
3.4Determineanunknowndimensionofarightcone,rightprism,rightpyramid,orspheregiventheSAorVandremainingdimensions.
3.5SolveaproblemthatinvolvesSAorV.
3.6Comparetheformula/relationshipbetweenvolumesofrightconesandrightcylindersorrightprismsandrightpyramids.
[C]Communication[PS]ProblemSolving,[CN]Connections[R]Reasoning,[ME]MentalMathematics[T]Technology,andEstimation,[V]Visualization
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Key Terms Term Definition
Linearmeasurement.
Dimension
Length
Width
Height
Radius
Diameter
Perimeter
Linearfoot
Conversionfactor
Baseoftriangle
Heightofatriangle(altitude)
2-dimensional
Area
SurfaceArea
Squarefoot.
Geometricnet
3-dimensional
Base(orbasearea)ofafigure
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Term Definition
Volume
Cubiccentimetres(ccorcm3)
Millilitre
Litre
Gallon
Rectangle
Square
Parallelogram
Trapezoid
Circle
RectangularPrism(&Cube)
RightTriangularPrism
Pyramid(triangular,rectangular,square)
RightCone
RightCylinder
Sphere
Hemisphere
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UnitConversions(astheymayappearonanexamformulasheet) CommonImperial ImperialandMetric MetricLength 1𝑚𝑖𝑙𝑒 = 1760𝑦𝑎𝑟𝑑𝑠
1𝑚𝑖𝑙𝑒 = 5280𝑓𝑒𝑒𝑡1𝑦𝑎𝑟𝑑 = 3𝑓𝑒𝑒𝑡1𝑦𝑎𝑟𝑑 = 36𝑖𝑛𝑐ℎ𝑒𝑠1𝑓𝑜𝑜𝑡 = 12𝑖𝑛𝑐ℎ𝑒𝑠
1𝑚𝑖𝑙𝑒 ≈ 1.609𝑘𝑚1𝑦𝑎𝑟𝑑 ≈ 0.9144𝑚1𝑓𝑜𝑜𝑡 ≈ 0.3048𝑚1𝑓𝑜𝑜𝑡 ≈ 30.48𝑐𝑚1𝑖𝑛𝑐ℎ ≈ 2.54𝑐𝑚
1𝑘𝑚 = 1000𝑚1𝑚 = 100𝑐𝑚1𝑐𝑚 = 10𝑚𝑚
Mass(Weight)
1𝑡𝑜𝑛 = 2000𝑝𝑜𝑢𝑛𝑑𝑠1𝑝𝑜𝑢𝑛𝑑 = 16𝑜𝑢𝑛𝑐𝑒𝑠
1𝑝𝑜𝑢𝑛𝑑 ≈ 0.454𝑘𝑔1𝑜𝑢𝑛𝑐𝑒 ≈ 28.35𝑔
1𝑡 = 1000𝑘𝑔1𝑘𝑔 = 1000𝑔
CommonAbbreviations
𝑚𝑖𝑙𝑒 = 𝑚𝑖𝑦𝑎𝑟𝑑 = 𝑦𝑑𝑡𝑜𝑛 = 𝑡𝑜𝑛𝑓𝑒𝑒𝑡 = 𝑓𝑡𝑜𝑟′𝑖𝑛𝑐ℎ = 𝑖𝑛𝑜𝑟"𝑝𝑜𝑢𝑛𝑑 = 𝑙𝑏𝑜𝑢𝑛𝑐𝑒 = 𝑜𝑧
𝑘𝑖𝑙𝑜𝑚𝑒𝑡𝑟𝑒 = 𝑘𝑚𝑚𝑒𝑡𝑟𝑒 = 𝑚𝑐𝑒𝑛𝑡𝑖𝑚𝑒𝑡𝑟𝑒 = 𝑐𝑚𝑚𝑖𝑙𝑙𝑖𝑚𝑒𝑡𝑟𝑒 = 𝑚𝑚𝑡𝑜𝑛𝑛𝑒(𝑚𝑒𝑡𝑟𝑖𝑐𝑡𝑜𝑛) = 𝑡𝑔𝑟𝑎𝑚 = 𝑔
Formula
Triangles LinesTrigonometry:
𝑠𝑖𝑛𝐴 =𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒
ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
𝑐𝑜𝑠𝐴 =𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡ℎ𝑦𝑝𝑜𝑡𝑒𝑛𝑢𝑠𝑒
𝑡𝑎𝑛𝐴 =𝑜𝑝𝑝𝑜𝑠𝑖𝑡𝑒𝑎𝑑𝑗𝑎𝑐𝑒𝑛𝑡
PythagoreanTheorem:𝑎2 + 𝑏2 = 𝑐2
Theequationofaline:Slope-interceptform:
𝑦 = 𝑚𝑥 + 𝑏StandardForm:
𝐴𝑥 + 𝐵𝑦 + 𝐶 = 0Point-slopeform:
𝑦 − 𝑦1 = 𝑚(𝑥 − 𝑥1)Slopeformula:
𝑚 =𝑦2 − 𝑦1𝑥2 − 𝑥1
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2-DimensionalFigure Perimeter AreaRectangle
𝑃 = 2𝑙 + 2𝑤or
𝑃 = 2(𝑙 + 𝑤)
𝐴 = 𝑙𝑤
Triangle
𝑃 = 𝑎 + 𝑏 + 𝑐
𝐴 =𝑏ℎ2
or
𝐴 =12𝑏ℎ
Circle
𝐶 = 2𝜋𝑟or
𝐶 = 𝜋𝑑
𝐴 = 𝜋𝑟2
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3-Dimensionalfigures:RightCylinder:
𝐴FGH = 𝜋𝑟2
𝐴IGFFGJ = 𝜋𝑟2𝐴KLMN = 2𝜋𝑟ℎ
𝑆𝐴FGFPQ = 2𝜋𝑟2 + 2𝜋𝑟ℎ
Net:
𝑉 = (𝐵𝑎𝑠𝑒𝐴𝑟𝑒𝑎)ℎ
Sphere:
Sphere:𝑆𝐴 = 4𝜋𝑟2
𝑉 =43𝜋𝑟
U
Hemisphere:
Hemisphere:𝑆𝐴 = 3𝜋𝑟2
𝑉 =23𝜋𝑟
U
Cone:
Side:𝐴 = 𝜋𝑟𝑠Base:𝐴 = 𝜋𝑟2
𝑆𝐴 = 𝜋𝑟2 + 𝜋𝑟𝑠
Net:
𝑉 =13(𝜋𝑟2)ℎ
Square-BasedPyramid:
𝐴FWLPXYQN =12𝑏𝑠
𝐴IPKN = 𝑏2
𝑆𝐴 = 2𝑏𝑠 + 𝑏2
Net:
𝑉 =13(𝑏𝑎𝑠𝑒𝑎𝑟𝑒𝑎)ℎ
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Rectangular(Right)Prism:
𝑆𝐴 = 2(ℎ𝑙 + 𝑙𝑤 + ℎ𝑤)
Net:
𝑉 = 𝑙𝑤ℎ
Or𝑉 = (𝑏𝑎𝑠𝑒𝑎𝑟𝑒𝑎)ℎ
TriangularPrism
𝑆𝐴 = 𝑠𝑢𝑚𝑜𝑓𝑎𝑙𝑙𝑓𝑎𝑐𝑒𝑠
Net:
𝑉 = (𝑏𝑎𝑠𝑒𝑎𝑟𝑒𝑎)ℎ
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MeasurementinTwoSystems.
TheInternationalSystemofUnits(SI)(MetricSystem)
SystèmeInternationald’unités
TheImperialSystemofUnits
History:FormallycalledSystemInternationalebutmorecommonlycalledTHEMETRICSYSTEM.Basedonthemetre.Onemeterisdefinedasthedistancelighttravelsin1/299792458ofasecond.
History:ThesystemusedbytheBritishEmpireandthereforemanyCommonwealthcountriesformanyyears.Tothisdaymuchdailyworkintradesisstilldoneusingtheimperialsystem.Mosttechnicalwork,however,usesthemetricsystem.
Prefixes:Prefixesareaddedtothebaseunitstobeusedwithsmallerorlargermeasurements.teragigamegakilohectodecaBASEUNIT(metre/gram/litre)decicentimillimicronanopico
Some useful conversions:
1 inch = 2.54 cm 1 foot = 30.5 cm (30.48) 1 yard = 3 feet 1 yard = 0.915 m 1 mile = 1760 yards 1 mile = 1.6 km 1 kg = 2.2 lbs 1 litre = 1.06 quarts (US) 1 gallon (US)= 3.79 litres
[1 gallon (UK)=4.55 litres]
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TheImperialSystemofUnitsUNIT
QUANTITYMEASURED(circleone)
REPRESENTATIVEEXAMPLE
orREFERENT(acomparisonyoucoulduse)
3EXAMPLESOFOBJECTSYOUWOULDMEASUREUSINGTHISUNIT
INCH
MASS?VOLUME?DISTANCE?
1.2.3.
FOOT
MASS?VOLUME?DISTANCE?
1.2.3.
YARD
MASS?VOLUME?DISTANCE?
1.2.3.
MILE
MASS?VOLUME?DISTANCE?
1.2.3.
GALLON
MASS?VOLUME?DISTANCE?
Thelargeplasticjugofmilkatthegrocerystore.
1.2.3.
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ConvertingBetweenUnitsWithintheImperialSystemConversionFactor:Multiplyingordividingbythisnumberallowsustoconvertfromoneunittoanother.Eg.Convert57inchestofeet.
57𝑖𝑛𝑐ℎ𝑒𝑠 ×1𝑓𝑜𝑜𝑡
12𝑖𝑛𝑐ℎ𝑒𝑠 =5712 𝑓𝑒𝑒𝑡
4 ^_`= 4 U
afeet
OneUnitConversionsConvertthefollowing.Answerinexactform(fractionornon-roundeddecimal).
1. 3yd.=___________feet.3yd× 3ft
1yd=9ft
2. 15yd.=___________feet. 3. 12.5yd.=___________feet.
4. 12ft.=___________yards. 5. 2.25ft.=___________inches.2.25ft.× 12in
1ft=27in
6. 136ft.=___________yards.
7. 8ft.=___________inches. 8. 2.75ft.=___________inches. 9. 4.8ft=___________inches.
10. 36in.=___________feet. 11. 140in.=___________feet. 12. 2016in=___________feet.
13. 2mi.=___________yards. 14. 4.2mi.=___________feet. 15. 1500yd.=___________miles.
16. 5250yd.=___________inches. 17. 160oz.=___________pounds. 18. 220oz.=___________pounds.
19. 4lb.=___________ounces. 20. 2.25lb.=___________ounces. 21. 6000lb.=___________tons.
22. Mr.Splaced32yardsticksendtoendacrosshisfrontyard.Findthewidthofhisyardinfeet.
23. Maisycanfit8blocksofbutterinherbackpack.Butterissoldin1poundblocks.HowmanyouncesdoesMaisycarry?
Usethenumbersinthetableonpage5.
1𝑓𝑜𝑜𝑡12𝑖𝑛𝑐ℎ𝑒𝑠
The unit on top is the one you are converting to!
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24. AuntieDeeismakingaframeforaphotograph.Theouterdimensionsare3ft.by5ft.Howmanyinchesofframemustshepurchase?
25. Mr.Jwantstoupdatehislivingroomwithcrownmoulding.Theroomisrectangularandmeasures180in.by260in.Mouldingissoldbythefootandcosts$2.19perlinearfoot.Whatisthecostofmouldingrequired(notincludinganytaxes)?
Converteachofthefollowingmeasurementstotheindicatedunits.26. 140feettoyardsandfeet.
Recall: 3yd=1ft140ft×_iM
UjF
=1403 𝑦𝑑
= 46 `U𝑦𝑑
140ft=46ydand2ft.
27. 256feettoyardsandfeet. 28. 356inchestoyards,feetandinches
29. 142inchestofeetandinches. 30. 204inchestoyardsandfeet. 31. 84260ouncestotons,poundsandounces.
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32. ShelbytheFrenchBullDogneedsanoutdoorareatorun.Benplansonbuildingherthepenbelow.Thefencingmaterialissoldbythelinearfootbuthismeasuringtapeonlyshowsinches.Howmanyfeetwillheneedtopurchase?
33. Convertyouranswerabovetoyards,feetandinches.
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34. Whatarethedimensionsoftherectangularcarpetbelowinfeet?
35. Ifthecarpetissoldfor$4.25persquarefoot,whatisthecostofcarpetrequired?Include12%tax.
36. Whatistheperimeterofthegardenshedinyardsandfeet?
37. Theshedcoversone-thirdoftheareaoftheyard.Howmanysquarefeetofsod(grass)areshownintheyardabove?
38. Sod-Warehousesellssodbytheroll.Eachrollis1footwideand4feetlong.Eachrollsellsfor$2.75.whatisthecost(including12%tax)tobuysodfortheyard?
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TwoUnitConversions{Becomfortableworkinginfractionformandalwaysreduce.}YouwillneedtouseTWOconversionfactors.Simplyfollowthestepsforoneunitconversions,thenrepeat.Eg.Convert58inchestoyards.�58𝑖𝑛𝑐ℎ𝑒𝑠 × _jGGF
_`LXmnNK= op
_`𝑓𝑒𝑒𝑡
�op
_`𝑓𝑒𝑒𝑡 × _iPWM
UjNNF= op
Uq𝑦𝑎𝑟𝑑𝑠
= 1 ``
Uq𝑦𝑎𝑟𝑑𝑠= 1 __
_p𝑦𝑎𝑟𝑑𝑠
39. 6025feet=_________miles
6025feet× 1yard
3feet= 6025
3yards
60253yards× 1mile
1760yards= qw`o
o`pwmiles
1 7455280
= 1 1491056
𝑚𝑖𝑙𝑒𝑠
40. 123450feet=_________miles
41. 2 12miles=______________inches.
42. 3.25yards=_________inches
43. 15 23yards=_________inches
473yd× 3ft
1yd× 12in
1ft= (ax)(U)(_`)
Uinches
=564inches
44. 24 13yards=_________inches
45. Acabinetmakerisusing1”x3”edgegrainfirtomakesomecabinetdoors.Hepurchased42 2
3yardsonCraig’slist.How
manyinchesdidhebuy?
46. Garyisbuildingpictureframestosellinamarket.Hehas75yardsofmaterialandwillmakesquareframeswithsidelengthsof14inches.Howmanyframescanhemake?
Mr.J’smeasuringwheelclicksonceforeveryyardittravels.Onawalktoschool,thewheelclicks35200times.
47. Howmanyinchesdoeshewalk?
48. Howmanymiles?
49. **Apieceofpaperisfoldedinhalfrepeatedly.Thepaperhasathicknessof1250".Howmanyyards
thickwillthepaperbeafter20folds?
ConversionFactors:
Step� _jGGF_`LXmnNK
Step � _iPWMUjNNF
The unit on top is the one you are converting to!
Note: I combined both steps into one equation here.
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ConversionswithNon-linearMeasurements.
50. Howdoyoucalculatetheareaofasquare?
51. Whatistheareaofthesquaretotheleftinsquare-feet?
52. Whatisthesidelengthofthesquareininches?
53. Whatistheareainsquareinches?
54. Toconverttheareaofafigurefromsquarefeettosquareinches,whatcalculationsmustyouperform?
55. Arectangularplotoflandhasdimensionsof0.5milesby0.4miles.Whatistheareainft2?
56. Toconverttheareaofafigurefromsquaremilestosquarefeet,whatcalculationsmustyouperform?
57. Apizzahasanareaof1.5ft2.Ifthepizzaistobeslicedintosixequalslices,howmanysquareinchesiseachslice?
58. Acircularcarpethasanareaof100𝜋ft2(approximately314ft2).Whatisthelengthoftheradiusininches?
59. Thecross-sectionofaconcreteundergroundpipeisshownbelow.Calculatetheareaoftheinner(open)partofthepipetothenearestin2.
60. Thepipeinthepreviousquestionhasconcretewallsthatare5feetthick.Calculatethecross-sectionalareaofconcretetothenearestin2.
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TheInternationalSystemofUnits(SI)UNIT QUANTITY
MEASUREDREPRESENTATIVEEXAMPLE 3EXAMPLESOFOBJECTSYOUWOULDMEASURE
USINGTHISUNITMilligram
MASS?VOLUME?DISTANCE?
ONEGRAINOFSALT
1.
2.
3.
Gram MASS?VOLUME?DISTANCE?
ONEPAPERCLIP
1.
2.
3.
Kilogram MASS?VOLUME?DISTANCE?
ONEPINEAPPLE
1.
2.
3.
Millilitre MASS?VOLUME?DISTANCE?
1.
2.
3.
Litre MASS?VOLUME?DISTANCE?
1.
2.
3.
Millimetre MASS?VOLUME?DISTANCE?
1.
2.
3.
Centimetre MASS?VOLUME?DISTANCE?
1.
2.
3.
Metre MASS?VOLUME?DISTANCE?
1.
2.
3.
Kilometre MASS?VOLUME?DISTANCE?
1.
2.
3.
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ConvertingBetweenUnitsintheMetricSystem(SI)ConversionFactor:Multiplyingordividingbythisnumberallowsustoconvertfromoneunittoanother.Eg.Convert230mmtocm.
230𝑚𝑚 ×1𝑐𝑚10𝑚𝑚 = 23𝑐𝑚
OneUnitConversionsConvertthefollowing.Answertothenearesttenthwhennecessary.
61. 1250mm=___________cm
1250mm× 1mJ
10JJ=125cm
Or...simplymovethedecimaloneplacetotheleft.
62. 37.25m=___________cm
63. 0.8cm=___________mm.
64. 138m=___________mm 65. 1508cm=___________m 66. 3.28cm=___________mm
67. Acirclehasaradiusof10cm.Findthecircumferenceofthecircleinmillimetres.
68. Afarmerbuildsafencearoundarectangularsheeppen.Thepenis5metreslongand7metreswide.Whatistheperimeterofthepenincentimetres?
69. Findtheheightofatrianglewithabaseof12cmandanareaof75cm2.Answerinmillimetres.
Usethenumbersinthetableonpage5.
1𝑐𝑚10𝑚𝑚
The unit on top is the one you are converting to!
Metric conversions can be made by moving the decimal left or right. Imperial conversions cannot.
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Two(orthree)UnitConversionsUsetwoconversionfactorstomakenecessaryconversions.Roundtothenearesttenthofaunitifnecessary.
70. Convert3.45mtomm. 71. Convert12.357kmtom. 72. Convert176mmtom.
73. Convert1.365kmtomm. 74. Convert17 15mtomm. 75. Convert3
4kmtocm.
76. Thepoliovirusisabout30nanometersindiameter.Thatis0.000000030m.Howmanymillimetresindiameteristhevirus.
77. TheGreatWallofMingDynastyinChinahasbeenmeasuredtobe8851.8kmlong.Approximatelyhowmanycentimetresisthis?
78. Astandardvolleyballcourtis18mlongand9mwide.Findtheareainsquaremillimetres.
79. 2m+30cm+4mm =__________________mm
80. 1.35km+125m+40cm =__________________m
81. 1.35km+125m+120mm =__________________cm
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UnitConversionbetweenSystemsOne-StepConversions:Usethetableonpage5.Writetheconversionfactorsasaratio(watchtheunits!).Converteachofthefollowing.Roundtothenearesttenth.
82. 50mi=_____________kmUse:1.609}J
1JL(fromreferencepage)
50mi×1.609km1mi =80.45km
≅80.5km
83. 185lb=___________kg 84. 150m=____________yd
85. 72in=_____________cm 86. 42𝑜𝑧 = _____________𝑔 87. 1245km=_____________mi
Two-SteporThree-StepConversions:Converteachofthefollowing.Roundtothenearesttenth.
88. 42km=__________________ft � Convert from kmàmi � Convert from mi à ft
42km×1mi
1.609km×5280ft1mi
≅137824.7ft
89. 54m=____________in 90. 1250g=______________lb
91. Answerthequestionaboveusingadifferentconversionstrategy.
92. 4.25km=_____________in 93. 1.3tons=_____________kg
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Convertthefollowing.Exactanswersorroundtothenearesthundredthwhennecessary.
94. 12𝑙𝑏𝑠3𝑜𝑧 = _________𝑘𝑔�Convert3oztolbs.
3𝑜𝑧 ×1𝑙𝑏16𝑜𝑧 = 0.1875𝑙𝑏
�Add:12 + 0.1875 = 12.1875𝑙𝑏�12.1875𝑙𝑏 × w.aoa}Y
_QI= 5.53kg
95. 2𝑙𝑏𝑠14𝑜𝑧 = _________𝑘𝑔 96. 7𝑙𝑏𝑠8𝑜𝑧 = _________𝑔
97. 12’6”=_________m 98. 8yd3’=_________m 99. 14m28cm=__________yd
100. Answerthequestionaboveusingadifferentconversionstrategy.
101. Answerthequestionaboveusingadifferentconversionstrategy.
102. Answerthequestionaboveusingadifferentconversionstrategy.
103. Apizzahasacircumferenceof5feet3inches.Findthediameterincentimetres.
104. Avolleyballhasadiameterof2feet2inches.Findthecircumferenceoftheballatitswidestpoint.Answertothenearestinch.
105. Mr.Jneeds2m,41cmand3mmofedgegrainfirtomakeeachofhiscabinetdoors.Howmanylinearfeetdoesheneedtomakehis8doors?
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Geometryof3-Dfigures.Familiarizeyourselfwiththeshapes,namesandformulasatthebeginningofthisbooklet.Usingthereferencepageatthebeginningofthisunit.
• Choosetherightformula.• Fillinallknownvaluesintotheformula.• Calculate(rememberBEDMAS).
SurfaceAreaAreaisthetwo-dimensionalsizeofasurface.Considertheareathatthisbookletiscoveringonthesurfacebelowit(unlessyouareonacomputerofcourse).Thesurfaceareaofasolidisthetotalareaofitsexposedsurfaces.Consideracommoncerealbox.Ifyouunfoldedthesides,top,bottom,frontandback...howmuchareaonyourdeskwoulditcover?Thatwouldbethesurfaceareaofthebox.
127. Refertopage5toanswerthefollowingquestion.
Findthesurfaceareaoftherectangularprismbelowtothenearestsquaremetre.
128. Refertopage5toanswerthefollowingquestion.
Findthesurfaceareaofthesquarepyramidbelowtothenearesttensquareinches..
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Findthesurfaceareaoftherectangularprismbelowtothenearestsquaremetre.
𝑆𝐴 = 2(ℎ𝑙 + 𝑙𝑤 + ℎ𝑤)𝑆𝐴 = 2[(1.5 × 3) + (3 × 2) + (1.5 × 2)]𝑆𝐴 = 2[4.5 + 6 + 3]𝑆𝐴 = 27𝑚`
Findthesurfaceareaofthesquarepyramidbelowtothenearesttensquareinches..
𝐴 = 2𝑏𝑠 + 𝑏` Need‘s’𝐴 = 2(75)(𝑠) + (75)` Use𝑎` + 𝑏` = 𝑐` 37.52 + 302 = 𝑠2 𝑠 = 48.0𝐴 = 2(75)(48.0) + (75)`𝐴 ≅ 12830𝑠qin
Calculatethesurfaceareaofthefollowingfigures.Answersshouldbegivenasindicated.129. Nearestsquareinch.
130. Nearestsquareinch.
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Calculatethesurfaceareaofthefollowingfigures.Answersshouldbegivenasindicated.131. Nearestsquaremillimetre.
132. Nearestsquarecentimetre.
133. Nearestsquarefoot..
134. Nearestsquarefoot.
135. Calculatethesurfaceareaofaconewithaheightof10cmandabasediameterof12cm.Answertothenearestsquarecentimetre.
136. Aconehasabaseradiusof15inchesandasurfaceareaof1650squareinches.Findtheslantheightoftheconetothenearestinch.
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137. Frankneedstofindthesurfaceareaoftheplaygroundequipmentbelowsohecanestimatehowmuchpainttobuy.Explaintheprocessheshoulduse(hewillnotpaintthebottom).
Explain________________________________________________________________________________________________________________________________________________________________________________________________________________________________
138. Findthesurfaceareaofthefiguretothelefttothenearestsquareinch.
139. Onequartofpaint(asmallcan)covers87.5sqft.HowmanyquartswillFrankneedtobuy?
140. Findthesurfaceareaoftheconcretecurbbelow(allsurfaces).Answertothenearestsquarecentimetre.
141. Calculatethesurfaceareaofthehexagonalprism(regular)tothenearestsquaremetre.
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VolumeVolumeistheamountof3-dimensionalspacethatafigureoccupiesorcontains.Considerthecerealbox.The“amount”ofBeaconBitsthatfitinsidetheboxisitsvolume.Thisisoftenreferedtoasthecapacityofacontainer.
142. Challenge:IfeachBeaconBitisacube1cmby1cmby1cm,howmanyBitswouldfitinthebox?Startbyfindingouthowmanywouldfitinthebottomlayer.
143. Refertopage5toanswerthefollowingquestion.
Findthevolumeoftheboxtothenearestcm3.
144. Refertopage5toanswerthefollowingquestion.
Findthevolumeoftheconetothenearestcubicinch.
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Findthevolumeoftheboxtothenearestcm3.
𝑉 = 𝑙𝑤ℎ
𝑉 = (27)(8)(35)𝑉 = 7560𝑐𝑚U
Findthevolumeoftheconetothenearestcubicinch.
𝑉 =13(𝜋𝑟`)ℎ
𝑉 =𝜋(55)`(75)
3
𝑉 =226875𝜋
3 = 75625𝜋 ≅ 237583𝑠𝑞𝑖𝑛
145. Usingtheformulaforthevolumeofarectangularprism,𝑉 = 𝑙𝑤ℎ,explainwhytheunitsforvolumeare“cubed”.
146. Refertopage5.Comparetheformulastocalculatevolumeofrightprisms,rightcylinders,andtriangularprisms.Whatdotheyallhaveincommon?
147. Timothyisbuildingagardenwaterfountainintheshapeofa“truncated”squarepyramid.Describehowyouwouldfindthevolumeofconcreterequiredtobuildthisfountain.
148. Findthevolumetothenearesttenthofmetre.
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Calculatethevolumeofthefollowingfigures.Answersshouldbegivenasindicated.149. Cubiccentimetres.
150. Cubiccentimetres.
151. Cubicfeet.
152. Cubicmetres.
153. Nearesttenthofacubicmetre.
154. Aspraynozzleproducesacone-shapedspraypattern.Findthevolumeoftheconeifthenozzleis12feetabovethegroundandproducesacirclewithadiameterof16feet.(Nearestcubicfoot)
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155. Findthevolumetothenearestcubicinch.
156. Ifthepyramidtotheleftisenlargedbyafactorof2,whatwillthenewvolumebe?
Canyoumakearule(formula)forthis?
157. Asquare-basedpyramidhasavolumeof250cubicyardsandaheightof30feet.Findthesidelengthofthesquarebasetothenearestfoot.
158. Aspherehasavolumeof3000m3.Findtheradiusofthespheretothenearestmetre.
159. Charlieneedstopaintthecompositeshapebelow.Beforehepurchasespaintheneedstocalculatethesurfaceareatothenearestsquarefoot.Thebottomdoesnotneedtobepainted.Howmanysquarefeetdoesheneedtopaint?
160. Findthevolumeofgravelinthepiletothenearestcubicyard.
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161. Findasphericalobjectandmeasurethediameter.Calculatethesurfaceareaofyourobject.Drawaneatanddetaileddiagramshowingyourobjectandmeasurement.Recordallmeasurementstothenearesttenthofacentimetre.Roundyouranswertothenearestsquarecentimetre.
162. Findaconicalobject.Makeappropriatemeasurementstothenearesttenthofacentimetre.Drawaneatanddetaileddiagramshowingyourobjectandmeasurements.Calculatethevolumeoftheconetothenearestcubiccentimetre.
163. Onegallonofpaintcoversapproximately350sq-ft.Howmanydecorativeballscanyoupaintwitha5-gallonbucketofpaintifeachballhasaradiusof12cm.
164. Acylindricalcanholds3tennisballs.Thediameterofatennisballis2½inches.Calculatethevolumeofairinthecansurroundingthe3balls.Thecanisdesignedtoholdexactlythreetennisballsintermsofheightanddiameter.(Nearesttenthofacubicinch).
165. Asectionofconcretepipehasaninsidediameterof2.2mandanoutsidediameterof2.5m.Findthecross-sectionalareaofexposedconcreteforoneendofthepipe.
166. Aspherehasasurfaceareaof260𝜋squarefeet.Findtheexactradiusofthesphere.
167. Aspherehasasurfaceareaof289𝜋squareinches.Findtheradiusofthespheretothenearesttenthofaninch.
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168. Belowisamodelofastandardroomatastoragefacility.Theinteriorwallsaretobepainted.Theroommeasures18’by24’andthewallheightis8’.Thedoorisstandardheightandwidth(36”by80”).Findtheinteriorsurfaceareaofthewalls.
Checkoutthehugeaquarium!Mr.Jwantstoswimthefishessoheisbuildingthisaquariuminhishome.
169. Calculatethevolumeofconcreteinthefloorofthe
aquariumincubicfeet.
170. Calculatethemassofthefloorifconcretehasamassof2400kgpercubicmetre.
171. Calculatetheareaofacrylic(aquariumwall)requiredtobuildthisstructure.
172. Sheetsofacrylicsellfor$45/sqft.Ifhecouldactuallyfindsheetsthissize,whatwouldbethecost(beforetaxes)?
173. Howmanylitresofwaterdoesthetankhold?Howmanygallons?Note:1𝑐𝑚U = 1𝑚𝑙, 1000𝑚𝑙 = 1𝑙𝑖𝑡𝑟𝑒,1𝑔𝑎𝑙𝑙𝑜𝑛 = 3.785𝑙𝑖𝑡𝑟𝑒𝑠
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174. Aspherehasavolumeof256�3cm3.Findtheexactradius
ofthesphere.
175. Asquare-basedpyramidwithaheightof10metreshasavolumeof300m3.Findtheexactsidelengthofthebase.
176. Findtheheightofacylinderifithasavolumeof1200cm3andaradiusof12cm.Answertothenearesttenthofacentimetre.
177. Findtheexactvolumeoftherightconebelow.Ithasaheightof10cmandaradiusof5cm.
178. Findtheexactvolumeofacylinderwiththesameheightandradiusastheconeinthepreviousquestion.
179. Whatistheratioofvolumesforthetwofiguresintheprevioustwoquestions?
180. Findthevolumeoftherightprismbelow.Answertothenearestcubicinch.
181. Belowisarightpyramidwiththesamebaseandheightastheprisminthepreviousquestion.Findthevolumetothenearestcubicinch.
182. Whatistheratioofvolumesforthetwopreviousfigures?
183. Ingeneral,whatistherelationshipbetweenthevolumesofrightpyramidsandrightprismswiththesamedimensions?
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Answers:1. 9ft2. 45ft3. 37 _
`or37.5ft
4. 4yd5. 27inches6. 45 _
Uyd
7. 96𝑖𝑛8. 33in9. 57.6in10. 3ft11. 11 `
U𝑓𝑡
12. 168ft13. 3520yd14. 22176ft15. xo
ppmiles
16. 189000in17. 10lbs18. 13 U
aor13.75lbs
19. 64oz20. 36oz21. 3tons22. 96’23. 128oz24. 192”25. $162.06for74’26. 46yd,2ft27. 85yd,1ft28. 9yd,2ft,8in29. 11’10“30. 5yd,2ft31. 2tons,1266lbsand4oz32. 74ft33. 24yd,2ft34. 6’x7’35. $199.9236. 13yd,1ft37. 192sqft38. $147.84for48rolls39. 1 149
1056𝑚𝑖𝑙𝑒𝑠(about1.141
miles)40. 23 67
176≅ 23.4𝑚𝑖𝑙𝑒𝑠
41. 158400”42. 117”43. 564”44. 876”45. 1536”46. 48frames47. 1267200”48. 20miles49. 116.5yd50. 𝐴 = 𝑙𝑤51. 9sqft52. 36in53. 1296sqin
54. Multiplybytheconversionfactor(12)twice.Thatis,multiplyby122
55. 5575680sqft56. Multiplyby(5280)257. 36sqin58. 120”59. 101788sqin60. 79168sqin61. 125cm62. 3725cm63. 8mm64. 138000mm65. 15.1m66. 32.8mm67. 628mm68. 2400cm69. 125mm70. 3450mm71. 12357m72. 0.2m73. 1365000mm74. 17200mm75. 75000cm76. 0.00003mm77. 885180000cm78. 162000000mm279. 2304mm80. 1475.4m81. 147512cm82. 80.5km83. 84.0kg84. 164.0yd85. 182.9cm86. 1190.7g87. 773.8miles88. 137824.7ft89. 2126.0in90. 2.8lbs91. 137795.3ft92. 167322.8in93. 1180.4kg94. 5.53kg95. 1.31kg96. 3402g97. 3.81m98. 8.23m99. 15.62yd100. 3.81m101. Tryyards
àfeetàmetres102. Trymàcm
àinchesàyards103. 50.94cm104. 82”105. 66 _
U=66.33linearft.
106. Youranswershere.107. Youranswershere.108. Youranswershere.109. Youranswershere.110. Trundlewheel.111. Verniercalipers.112. Micrometer.113. Inches,cm,mm.114. Eg.Measuringtape.Cm,
inches(andfractionsthereof)
115. Eg.Measuringcup.Cups,ounces,ml,l
116. Eg.Volumetriccylinder.ml
117. Eg.2-panbalancescale.g,kg
118. Eg.Electronicscale.𝜇𝑔,mg,g
119. Diameter,distance.120. Volume.ml121. Diameter,distance.122. Onesetofclawsisfor
measuringinsidediameterssuchasinsideatube.Theotherisformeasuringoutsidediameter.
123. 1.97mm124. 3.15cm125. 3.68cm126. 0.40mm127. 27m2128. 12830sqin129. 81268sqin130. 19684sqin131. 1810mm2132. 86cm2133. 16965sqft134. 137sqft135. 333cm2136. 20”137. Findthesurfaceareaof
therectangularprism,addtheareaofthecurvedcylindricalsurface,subtractthebottomoftheprismandthetwocircles.
138. 41734sqin139. Frankshouldbuy4
quarts.140. 739655cm2(with
bottom)478889cm2(withoutbottom)
141. 36m2142. 7560BeaconBits
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143. 7560cm3144. 237583cubicinches145. Thethreedimensions
haveunitssuchascentimetres.Ifwemultiply𝑐𝑚 × 𝑐𝑚 × 𝑐𝑚weget𝑐𝑚U.
146. Bottom(basearea)multipliedbytheheight.
147. Findthevolumeofthelargepyramidandsubtractthevolumeofthesmall(removed)pyramid.
148. 11.5m3149. 11058432cm3150. 4193205cm3151. 85cubicfeet152. 24.4m3153. 7.1m3154. 804cubicfeet155. 60cubicinches156. 480cubicinches157. 26ft158. 9m159. 269sqft160. 4yd3161. Youranswerhere.162. Youranswerhere.163. 897balls164. 12.3cubicinches165. 1.1m2166. Radiusis√65ft167. 8.5in168. 652sqft169. 448cubicfeetor12.69
m3170. 30446kg171. 616sqft172. $27720173. 76116l,20108gal174. 4cm175. 3√10m(approx9.49m)176. 2.7cm177. `ow
U𝜋cm3
178. 250𝜋cm3179. 1: 3or_
U
180. 212628cubicinches181. 70876cubicinches182. 1: 3or_
U
183. Pyramidsandconeswillhavevolumesequaltoone-thirdoftheircorrespondingprism.