Volume of Rotated Figures

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1、VolumeofRotatedFiguresTeacherNotesTopicArea:VolumeofSolidsbyShellMethodNCTMStandards:•Usetwo-dimensionalrepresentationsofthree-dimensionalobjectstovisualizeandsolveproblemssuchasthoseinvolvingsurfaceareaandvolume;•UseCartesiancoordinatesandothercoordinatesystems,suchasnavigational,polar,orsph

2、ericalsystems,toanalyzegeometricsituations;ObjectivesGivenaphotofile,studentswillbeabletofitanequationontothepictureandfindtheequationforthelineofbestfit.Usingtheirknowledgeofpolynomialfunctionsandintegralcalculus,thestudentswillfindthevolumeofafigureformedbyrotatingapolynomialaroundaspecifie

3、daxis.GettingStartedHavestudentsworkinpairstodeterminethecoordinatesofpointsusedtofindthelineofbestfitforapolynomialandusethisequationtosolveproblemsinvolvingrotationofsolids.Priortousingthisactivity:•Studentsshouldhaveanunderstandingofhowtofindaregressionline.•Studentsshouldhaveanunderstandi

4、ngofpolynomialfunctions.•Studentsshouldbeabletowriteandsolveanintegralgiventhefunctionwithupperandlowerbounds.Waysstudentscanprovideevidenceoflearning:•Studentswillbeabletousetheirknowledgeofgeometrytodetermineupperandlowerboundsforanintegral.•Studentswillbeabletofindthevolumeofafigureusingth

5、eshellmethod.Commonmistakestobeonthelookoutfor:•Studentsmayhavedifficultydeterminingupperandlowerbounds.•Studentsmayhavedifficultywiththeintegrationofapolynomial.•Studentsmayusethewrongpolynomialfortheintegration.Definitions:•Regression•UpperandLowerBounds•Integral©2010CASIOComputerCo.,LTD.Al

6、lRightReserved.Page-1-VolumeofRotatedFigures“HowTo”Thefollowingwillwalkyouthroughthekeystrokesandmenusrequiredtosuccessfullycompletethevolumeofrotatedfiguresactivity.ToopenabackgroundimageinPicturePlot:1.FromtheMainMenu,highlightthePicturePloticonandpresslorpress(.2.Pressq(OPEN)toopentheCASIO

7、folder.3.Theg3pfoldercontains47backgroundimages.PressNq(OPEN)toopenthefolder.Scrolldownthelistofimagesandhighlightthedesiredimage.Youwillbeusingthe“Pancakes”inthisactivity.Pressq(OPEN).©rimglow-Fotolia.comToplotspointsontheimageandcreatealist