1

Unit7ExtendingToThreeDimensions

Lesson1:WhatisArea?OpeningExerciseWhatisarea?Findtheareaoftherectanglepicturedbelow:

2

AreaFormulasYouNeedtoKnow!

Name Formula Diagram

AreaofaParallelogram

(thisincludesrectangles,rhombusesandsquares)

A bh=

AreaofaTriangle 12A bh=

Exercises1. Findthearea: 2. Findtheareaofasquarethathas adiagonallengthof 7 2 cm.3. Findtheexactareaofanequilateraltriangleinwhichthesidesmeasure4inches.

3

Example1Howdowefindtheareaofpolygonalregionswedonothaveformulasfor?Drawlinestoshowhowyoucandividethefollowingpolygonalregionsintofiguresyouknowtheareaformulasfor:

4

Example2Calculatetheareaoftheshadedfigurebelow.

Explainhowyoudeterminedtheareaofthefigure.Example3Arectanglewithdimensions21.6x12hasarighttrianglewithabaseof9.6andaheightof7.2cutoutoftherectangle.Findtheareaoftheshadedregion.Explainhowyoudeterminedtheareaoftheshadedregion.

5

Example4Twotriangles,ΔABC andΔDEF areshown.ThetwotrianglesoverlapformingΔDGC .ThebaseoffigureABGEFiscomprisedofsegmentsofthefollowinglengths:AD=4,DC=3,andCF=2.CalculatetheareaofthefigureABGEF.Explainhowyoudeterminedtheareaofthefigure.Example5Woodpiecesinthefollowingshapesandsizesarenailedtogetherinordertocreateasignintheshapeofanarrow.Thepiecesarenailedtogethersothattherectangularpieceoverlapswiththetriangularpieceby4in.Whatistheareaoftheregionintheshapeofthearrow?

6

Homework1. Findtheareaofthefollowingfigures: a. b.2. Twosquareswithsidelength5meetata

vertexandtogetherwith AB formatrianglewithbase6asshown.Findtheareaoftheshadedregion.

AB

7

Lesson2:AreaofaCircleOpeningExercise

AreaofaCircle

CircumferenceofaCircle

2A rπ=

C=2πr

Usingtheformulaslistedabove,answerthefollowing:1. Findtheexactareaandcircumferenceofacirclewitharadiusof7.2. Findtheexactcircumferenceofacirclethathasanareaof144π .3. Acirclehasacircumferenceof21.98meters.Finditsareatothenearesthundredth.

8

Checkoutthisvideoonhowtheformulafortheareaofacircleisderived:https://www.youtube.com/watch?v=YokKp3pwVFcExample1Thesideofasquareis20cmlong.a. Whatisthecircumferenceofthecirclewhenthecircleisinscribedwithinthe

square?Leaveanswerintermsofπ .b. Whatisthecircumferenceofthecirclewhenthesquareisinscribedwithinthe

circle?Leaveanswerasaradicalintermsofπ .

9

PopulationDensity=populationarea

Let’swatchavideotolearnaboutpopulationdensity!https://www.youtube.com/watch?v=Bbs-gwmAuGwExample2Using2015data,whichofthefollowingstatesismoredenselypopulated.Justifyyouranswer. NewYorkState Florida

Population:19,795,791 Population:20,271,272Area:47,126squaremiles Area:53,625squaremiles

10

Homework1. Findtheexactcircumferenceandareaofacirclethathasadiameterof22inches.2. Thecircumferenceofacircleis128π . Find the circle’s area in terms of π .3. Apatioconsistingoftwosemicirclesanda

squareisshowninthediagrambelow.Thelengthofeachsideofthesquareregionisrepresentedby2x.Writeanexpressionfortheareaoftheentirepatiointermsofxandπ .

4. In2009,therewere6342penguinsinIslaMartillo,Argentina.Theareaoftheisland

isapproximately47squareacres.Tothenearestwholenumber,whatwasthedensityofthepenguinpopulation?

5. In2011,therewere3223seaottersinMontereyBay,California.Thebayis

approximately77squaremiles.Tothenearestwholenumber,whatwasthedensityoftheseaotterpopulation?

11

Lesson3:CrossSectionsof3-DimensionalFiguresOpeningExerciseUsethediagramspicturedtohelpyouidentifythemissinginformationinthetable:

FigureandDescription SketchofFigurePrism

#ofbases:ShapeoftheBases:ShapeoftheLateralFaces:

Cylinder

#ofbases:ShapeoftheBases:

Pyramid

#ofbases:ShapeoftheBase:Shape of the Lateral Faces:

Cone

#ofbases:ShapeoftheBase:

Whatelsedoyounoticeabouttherelationshipbetweenthebasesofprismsandcylinders?Let’stakealookatthisvideoonCross-Sectionsof3-DimensionalShapes!https://learnzillion.com/lesson_plans/8121-visualize-cross-sections-of-prisms

12

Vocabulary

Term Definition Diagram

Base(BaseFace)

Thetwocongruent,parallelsidesofaprismorcylinder.

Edge

Asegmentthatisformedbytheintersectionoftwofacesofasolid.

Vertex

Apointwherethreeormoreedgesofasolidintersect.

LateralFace

Thefacesinageometricsolidthatarenotthebases.

Sliceor

CrossSection

Ageneralintersectionofaplaneandasolid.

CrossSectionParalleltotheBase

Whenthesliceisparalleltothebase,thecross-sectionisthesameshapeandsizeas

thebase.

RightPrism ObliquePrism

13

Example1Sketchtheindicatedcross-section:

Cross-sectionParalleltothe

Base

Cross-sectionPerpendiculartotheBase

ContainingtheAltitude

Example2Isthefiguregiventotherightacylinder?Explainwhyorwhynot.Example3Thefollowingarecross-sectionsthatareparalleltothebases.Sketchthefigurefromwhichthecross-sectionwastaken.a. b.

14

Example4 If we were to rotate the pictured rectangular region around the provided axis: the result would be a cylinder:Whatifwerotatedthistriangularregionaroundtheprovidedaxis?

15

Homework1. a. Thepicturedcylinderisanexampleofwhatkind

ofprism?

b. If 'AA wereperpendiculartotheplaneofthe base,thiswouldbewhatkindofprism?

c. Theregions ABCD and ' ' ' 'A B C D are_________________________. d. 'AA isa(n)_________________________.

e. Parallelogramregion ' 'BB C C isoneoffour_________________________.

2. Sketchthefigureformediftherectangularregionisrotatedaroundtheprovided

axis:

16

Lesson4:GeneralPyramidsandConesandTheirCross-SectionsOpeningExercisea. Identifytheshapeofthecross-sectionparalleltothebaseineachofthefigures

shownabove.Whatisdifferentaboutthesecross-sections?b. Identifytheshapeofthecross-sectioncontainingthealtitudeofeachofthefigures

shownabove.Willtheseshapesholdtrueforallgeneralcylindersandgeneralcones?

17

Example1RectanglesAandBaresimilar.IftheareaofAis 288mm ,whatistheareaofB?

Thecross-sectionofafigureisaslicethatistakenparalleltothebaseofthesolid.Inageneralcone,thecross-sectionwillalwaysbeafigurethatissimilartothebaseofthecone.Thevertexoftheconeisthecenterofdilation.

18

Example1Inthetriangularpyramid,aplanepassesthroughthepyramidsothatitisparalleltothebaseandresultsinthecross-sectionof ' ' 'A B CΔ .Iftheareaof ABCΔ is 225mm ,whatistheareaof ' ' 'A B CΔ ?Example2Inthefollowingtriangularpyramid,aplanepassesthroughthepyramidsothatitisparalleltothebaseandresultsinthecross-section ' ' 'A B CΔ .ThealtitudefromV isdrawn;theintersectionofthealtitudewiththebaseis X ,andtheintersectionofthealtitudewiththecross-sectionis 'X .Ifthedistancefrom X toV is18mm ,thedistancefrom 'X toV is12mm ,andtheareaof ' ' 'A B CΔ is 228mm ,whatistheareaof ABCΔ ?

19

Theorem Description Diagram

GeneralConeCross-SectionTheorem

Iftwogeneralconeshavethesamebaseareaandthesameheight,thencross-sectionsforthegeneralconesthesamedistancefromthevertex

havethesamearea.

Example3Thediagrambelowshowsacircularconeandageneralpyramid.Thebasesoftheconesareequalinarea,andthesolidshaveequalheights.

a. Sketchasliceineachconethatisparalleltothebaseoftheconeand 23

closertothevertexthanthebaseplane.

b. Iftheareaofthebaseofthecircularconeis 2616units ,findtheexactareaofthesliceshowninthepyramid.

20

Exercises1. Theareaofthebaseofaconeis 216in ,andtheheightis10in .Findtheareaofthe

cross-sectionthatisadistanceof5in fromthevertex.2. Thefollowingpyramidshaveequalaltitudes,andbothbasesareequalinareaand

arecoplanar.Bothpyramids’cross-sectionsarealsocoplanar.If 3 2BC = and' ' 2 3B C = ,andtheareaofTUVWXYZ is 230units ,whatistheareaofcross-section' ' ' 'A B C D ?

21

Homework1. Sketchthefigureformedifthetriangularregionisrotatedaroundtheprovidedaxis:

2. Ageneralconehasbasearea 236units .Findtheareaofthesliceofthecone

thatisparalleltothebaseand 23ofthewayfromthevertextothebase.

3. Ageneralhexagonalpyramidhasaheightof10in .Aslice2in abovethebasehasanareaof 216in .Findtheareaofthebase.

22

Lesson5:VolumeofGeneralCylindersOpeningExercise

Name Formula Diagram

VolumeofaPrism

V = Bh

B is the area of the base h is the height

VolumeofaPrism V = πr2h

Findthevolumeofthefollowingprisms:

1. 2.

3. Findthevolumeofthepicturedcircularcylindertothenearesthundredth.

23

AreaProperties VolumeProperties

1.Theareaofasetin2-dimensionsisanumbergreaterthanorequaltozerothatmeasuresthesizeofthesetandnottheshape.

1.Thevolumeofasetin3-dimensionsisanumbergreaterthanorequaltozerothatmeasuresthesizeofthesetandnottheshape.

2.Theareaofarectangleisgivenbytheformulalengthxwidth.Theareaofatriangleisgivenbytheformula½basexheight.Apolygonalregionistheunionoffinitelymanynon-overlappingtriangularregionsandhasareathesumoftheareasofthetriangles.

2.Arightrectangularortriangularprismhasvolumegivenbytheformulaareaofbasexheight.Arightprismistheunionoffinitelymanynon-overlappingrightrectangularortriangularprismsandhasvolumethesumofthevolumesoftheprisms.

3.Congruentregionshavethesamearea.

3.Congruentsolidshavethesamevolumes.

4.Theareaoftheunionoftworegionsisthesumoftheareasminustheareaoftheintersection:

4.Thevolumeoftheunionoftwosolidsisthesumofthevolumesminusthevolumeoftheintersection:

5.Theareaofthedifferenceoftworegionswhereoneiscontainedintheotheristhedifferenceoftheareas:

5.Thevolumeofthedifferenceoftwosolidswhereoneiscontainedintheotheristhedifferenceofthevolumes:

24

Example1 Asolidmetalprismhasarectangularbasewithsidesof4inchesand6inches,andaheightof4inches.Aholdintheshapeofacylinder,witharadiusof1inch,isdrilledthroughtheentirelengthoftherectangularprism.Whatistheapporoximatevolumeoftheremainingsolid,incubicinches?Example2 BlasdellPizzahasjustcreatedadeepdishpizzaandhasaskedyoutodesignanewpizzaboxsincetheiroldboxeswillnotbetallenough.Thenewpizzahasaradiusof8inchesandaheightof2inches.Tominimizethecostoftheboxandtopreservethequalityofthepizza,theywanttheboxtobeoneinchtallerthanthepizzaandanextrahalfinchoneachsideofthepizza.a. Determinethedimensionsofthebox.b. Determinethevolumeofthebox.c. Tothenearesttenth,howmuchofthebox’svolumeisnotbeingtakenupbythe

pizza?d. Approximatelywhatpercentageoftheboxisnotbeingused?

25

Example3Acan12centimeterstallfitsintoarubberizedcylindricalholderthatis11.5cmtall,including1cmforthethicknessofthebaseoftheholder.Thisthicknessoftherimoftheholderis1cm.Whatisthevolumeoftherubberizedmaterialthatmakesuptheholdertothenearesthundredth?

26

HomeworkFindthevolumeofthefollowingprisms.Leaveanswerintermsπ whennecessary:1. 2.3. Acylindericalstainlesssteelcolumnisusedtohideaventilationsysteminanew

building.Accordingtothespecifications,thediameterofthecolumncanbebetween30cmand95cm.Theheightistobe500cm.Whatisthedifferenceinvolumebetweenthelargestandsmallestpossiblecolumntothenearesttenth?

27

Lesson6:DimensionalAnalysisOpeningExerciseRecallthefollowingconversionsfromAlgebraandyourscienceclasses:

1meter=___________centimeters 1kilogram=___________gramsConvertthefollowing:1. 5cm=__________m 2. 3.2m=__________cm 3. 50.7kg=__________g 4. 37.21g=__________kg

28

ThefollowingisontheCommonCoreReferenceSheet:

Convertthefollowing:1. Howmanyfeetarein13yards?2. Howmanymilesarein6,600yards?3. Howmanygallonsarein10liters?4. Howmanycupsarein3quarts?

29

DensityFormula:

massdensityvolume

=

Whatdoesdensityreallymean?Let’swatchashortvideotogetabetterunderstanding!https://www.youtube.com/watch?v=ObFNsgZuGk0Example1Asquaremetalplatehasadensityof 310.2g/cm andweighs2.193kg .a. Calculatethevolumeoftheplate.b. Ifthebaseofthisplatehasanareaof 225cm ,determineitsthickness.

30

Homework1. Convert1,234millimeterstocentimeters.2. Convert78centimeterstokilometers.3. Convert32kilogramstograms.4. Howmanypoundsarein5,900grams?

31

Lesson7:DensityOpeningExerciseIn2011,theNationalScienceFoundationconductedagermstudy.Theyfoundthatthedirtiestiteminmosthomeswasthekitchenspongewith10millionbacteria.Giventhattheaveragekitchenspongeis0.5inby3inby5in,whatisthebacterialdensity?Example1Ashippingcontainerisintheshapeofarightrectangularprismwithalengthof12feet,awidthof8.5feet,andaheightof4feet.Thecontaineriscompletelyfilledwithcontentsthatweigh,onaverage,0.25poundpercubicfoot.Whatistheweight,inpounds,ofthecontentsinthecontainer?

32

Example2Acontractorneedstopurchase500bricks.Thedimensionsofeachbrickare5.1cmby10.2cmby20.3cm,andthedensityofeachbrickis1920kg/m3.Ifthemaximumcapacityofthecontractor’straileris900kg,canthetrailerholdtheweightofthe500bricks?Justifyyouranswer.Example3Treesthatarecutdownandstrippedoftheirbranchesfortimberareapproximatelycylindrical.Atimbercompanyspecializedinacertaintypeoftreethathasatypicaldiameterof50cmandatypicalheightofabout10meters.Thedensityofthewoodis380kilogramspercubicmeter,andthewoodcanbesoldbymassatarateof$4.75perkilogram.Determineandstatetheminimumnumberofwholetreesthatmustbesoldtoraiseatleast$50,000.

33

Lesson8:TheVolumeofPrismsandCylindersandCavalieri’sPrincipleOpeningExerciseThebasesofthefollowingtriangularprismT andrectangularprismR lieinthesameplane.Aplanethatisparalleltothebasesandalsoadistance3fromthebottombaseintersectsbothsolidsandcreatescross-sections 'T and 'R .a. FindArea( 'T ). b. FindArea( 'R ).c. FindVol(T ). d. FindVol(R ).e. Ifaheightotherthan3werechosenforthecross-section,wouldthecross- sectionalareaofeithersolidchange?

34

Cavalieri’sPrincipleGiventwosolidsthatareincludedbetweentwoparallelplanes,ifeveryplaneparalleltothetwoplanesintersectsbothsolidsincross-sectionsofequalarea,thenthevolumesofthetwosolidsareequal.HereareafewexamplesillustratingCavalieri’sPrinciple.Sinceeachgroupofsolidshavethesamealtitude,andthecross-sectionalareaisequalforallheights,eachofthegroupsshowssolidswithequalvolumes. http://demonstrations.wolfram.com/CavalierisPrinciple/

35

Example1Giventwostacksofquartersaspicturedinthefigurebelow,whatdoweknowabouttheirvolumes?Why?Example2Atriangularprismhasanisoscelesrighttriangularbasewithahypotenuseof 32 andaprismheightof15.Asquareprismhasaheightof15anditsvolumeisequaltothatofthetriangularprism.Whatarethedimensionsofthesquarebase,insimplestradicalform?

36

Exercises1. Findthevolumeofthefollowingoblique

hexagonalprism.

2. Findthevolumeofanobliquecircularcylinderthathasaradiusof5feetanda

heightof3feet.Roundtothenearesttenth.3. PrismsAandBhavethesamelengthand

width,butdifferentheights.IfthevolumeofPrismBis150cubicinchesgreaterthanthevolumeofPrismA,whatisthelengthofeachprism?

37

Homework1. MorgantellsyouthatCavalieri’sPrinciplecannotapplytothecylindersshown

belowbecausetheirbasesaredifferent.Doyouagreeordisagree?Explain.2. Anobliquecircularcylinderhasheight5andvolume45π .Findtheradiusof thecircularbase.

38

Lesson9:TheVolumeFormulaforPyramids,Cones,andSpheresOpeningExerciseUseCavalieri’sPrincipletoexplainwhyacircularcylinderwithabaseofradius5andaheightof10hasthesamevolumeasasquareprismwithedgelengths5 π andwhoseheightisalso10.Vocabulary

Term Definition Diagram

SlantHeight

Thedistancemeasuredalongalateralfacefromthebasetothevertexofapyramidorcone.Inthecaseofapyramid,theslantheightistheheightofthetriangularlateralface.

39

VolumeFormula

Solid Diagram VolumeFormula

Pyramid

13

V Bh=

whereBistheareaofthebaseandhistheheightofthepyramid

Exercises1. Findthevolumeofthefollowingpyramid:

2. Ifaregularpyramidhasatriangularbasethatisequilateralwithsidesmeasuring4

feet,anditsvolumeis 364 3 ft ,findtheheightofthepyramid.

40

VolumeFormula

Solid Diagram VolumeFormula

Cone

13

V Bh=

whereBistheareaofthebaseandhistheheightofthecone

Exercises1. Findthevolumeofthefollowingconeintermsofπ :

2. Iftheslantheightofaconeis26,andtheradiusofthebaseis10.Findthevolumeoftheconetothenearesttenth.

41

VolumeFormula

Solid Diagram VolumeFormula

Sphere

343

V r= π

whereristhelengthoftheradiusofthesphere

Exercise1. Snowglobesconsistofaglassspherethatisfilledwithliquidandothercontents.If

theinsideradiusofthesnowglobeis3inches,findtheapproximatevolumeofmaterialincubicinchesthatcanfitinside.

2. Anicecreamconeis11cmdeepand5cmacrosstheopeningofthecone.Two hemisphere-shapedscoopsoficecream,whichalsohaveadiameterof5cmare placedontopofthecone.Iftheicecreamweretomeltintothecone,willitoverflow?

42

Example1Aconefitsinsideacylindersothattheirbasesarethesame,asshowninthediagrambelow.Calculatethevolumethatisinsidethecylinderbutoutsidethecone.Giveanexactanswer.

43

Homework1. Findtheexactvolumeofthefollowingsolids: a. b. 2. AtthetopoftheWashingtonMonumentisasmallsquarepyramid,calleda

pyramidion.Thispyramidhasaheightof55.5feetwithbaseedgesofapproximately34.5feet.Whatisthevolumeofthepyramidion?Roundtothenearesttenth.

3. Ahemisphericaltankisfilledwithwaterandhasadiameterof10feet.Ifwater

weights62.4poundspercubicfoot,whatisthetotalweightofthewaterinafulltank,tothenearestpound?

44

Lesson10:ScalingPrincipleforVolumesOpeningExerciseGiventhesimilarfigurespictured,answerthefollowing:a. Calculatethevolumeofbothsolids.b. Findtheratioofthesideslengthsinsimplestform.c. Findtheratioofthethevolumesinsimplestform.d. Whatistherelationshipbetweenyouranswersfrompartsbandc?

45

Example1Giventhesimilarfigurespictured,answerthefollowing:a. Calculatethevolumeofbothsolids.b. Findtheratioofthesideslengthsinsimplestform.c. Findtheratioofthethevolumesinsimplestform.d. Whatistherelationshipbetweenyouranswersfrompartsbandc?SUMMARY:Iftwosimilarsolidshaveascalefactorofa:b,thenthesurfaceareashavearatioofa2:b2,andthevolumeshavearatioofa3:b3.Given2similarsolids: Scalefactor: RatioofSurfaceAreas: RatioofVolumes:

46

6

Exercises1. Twocircularcylindersaresimilar.Theratiooftheareasoftheirbasesis9:4 . Findtheratioofthevolumesofthesimilarsolids.2. Ageneralconehasaheightof6.Whatfraction ofthecone’svolumeisbetweenaplanecontaining thebaseandaparallelplanehalfwaybetweenthe vertexoftheconeandthebaseplane?3. RightcircularcylinderAhasavolumeof2700witharadiuslengthof3.Right

circularcylinderBissimilartocylinderAandhasavolumeof6400.FindtheradiuslengthofcylinderB.

47

Homework1. Coffeesoldatadelicomesinsimilar-shapedcups.Asmallcuphasaheightof4.2in

andalargecuphasaheightof5in .Thelargecoffeeholds12fluidounces.Howmuchcoffeeisinasmall-sizedcup?Roundyouranswertothenearesttenthofanounce.

2. Thefollowingsolidsaresimilar.Thevolumeofthefirst

solidis100.Findthevolumeofthesecondsolid.3. Acompanyusesrectangularboxestopackagesmallelectroniccomponentsfor

shipping.Theboxthatiscurrentlyusedcancontain500ofonetypeofcomponent.Thecompanywantstopackagetwiceasmanypiecesperbox.Michaelthinksthattheboxwillholdtwiceasmuchifitsdimensionsaredoubled.ShawndisagreesandsaysthatMichael’sideaprovidesaboxthatismuchtoolargefor1,000pieces.Explainwhyyouagreeordisagreewithoneoreitheroftheboys.Whatwouldyourecommendtothecompany?

48

Lesson11:ApplyingModelinginGeometricSituationsOpeningExerciseUsingthefollowingpictures:a. Identifythethree-dimesionalshapesthatmakeupthepicture.b. Drawthecross-sectioncontainingthealtitudeforeachoftheshapeslistedinparta.1.2. 3.

49

Example1Ifthealtitudeofthepapercontainerofasnowconeis3inchesandthediamteris2inches,calculatethevolumeoficeusedinthesnowcone.Roundyouranswertothenearesttenthofacubicinch.Example2Theofficialdiameterofatennisballis2.70inches.Ifthetennisballcontainerhasthesamediameterandaheightof8.2inches,whatpercentageofthespaceinthecontainerisnotbeingused?

50

Example3Walterwantstomake100candlesintheshapeofaconeforhisnewcandlebusiness.Themoldshownbelowwillbeusedtomakethecandles.Eachmoldwillhaveaheightof8inchesandadiameterof3inches.Tothenearestcubicinch,whatwillbethetotalvolumeof100candles?Waltergoestoahobbystoretobuythewaxforhiscandles.Thewaxcosts$0.10perounce.Iftheweightofthewaxis0.52ouncepercubicinch,howmuchwillitcostWaltertobuythewaxfor100candles?IfWalterspentatotalof$37.83forthemoldsandcharges$1.95foreachcandle,whatisWalter’sprofitafterselling100candles?

51

Example4Aboxof9identicalornamentsispackedtightlyasshownbelow.a. Findtheexactspacebeingusedbytheornaments.b. Findtheexactspacenotbeingusedbytheornaments.

52

Example5Awaterglasscanbemodeledbyatruncatedrightcone(aconewhichiscutparalleltoitsbase)asshownbelow.

Thediameterofthetopoftheglassis3inches,thediameteratthebottomoftheglassis2inches,andtheheightoftheglassis5inches.

Thebasewithadiameterof2inchesmustbeparalleltothebasewithadiameterof3inchesinordertofindtheheightofthecone.Explainwhy.Determineandstate,ininches,theheightofthelargercone.Determineandstate,tothenearesttenthofacubicinch,thevolumeofthewaterglass.

53

Example6Thewatertowerinthepictureismodeledbythetwo-dimensionalfigurebesideit.Thewatertoweriscomposedofahemisphere,acylinderandacone.LetCbethecenterofthehemisphereandletDbethecenterofthebaseofthecone.IfAC=8.5feet,BF=25feet,andm∠EFD = 47° ,determineandstate,tothenearestcubicfoot,thevolumeofthewatertower.Thewatertowerwasconstructedtoholdamaximumof400,000poundsofwater.Ifwaterweighs62.4poundspercubicfoot,canthewatertowerbefilledto85%ofitsvolumeandnotexceedtheweightlimit?Justifyyouranswer.