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1、ApplicationofDifferentiationRateofChangeExampleAsnowballismeltinganditsvolumeisdecreasingattherateof12.Whenitsradiusis6cm,finda)therateofchangeofitsradius,b)therateofchangeofitssurfacearea.TheradiusisdecreasingatarateofWhenr=6,ThesurfaceareaisdecreasingatarateofExampleThesurfaceareaofasoapbubbl

2、eincreasesataconstantrateof4.Findtherateatwhichthevolumeisincreasingwhenitsradiusis2cm.ExampleAninvertedhollowcircularconeofsemi-verticalangle30andheight30cmiscompletelyfilledwithwater.Thewaterthenbeginstoleakthroughasmallholeatthevertex.Initially,justasthewaterbeginstoleak,thedepthdecreasesata

3、rateof1cm/s.(i)Showthatthevolumeofwaterintheconeisgivenby,wherehisthedepthofwater.(ii)Findtherateatwhichthevolumeofwaterisdecreasinginitially.b)Assumethevolumeofwatercontinuestodecreaseatthesamerate.Whenthedepthis10cm,findtherateofdecreaseof(i)thedepth;and(ii)theareaofwatersurface.ExampleAnicep

4、illarintheshapeofcylinderismeltingsothatitsdiameterandheightaredecreasingattheratesof1cm/hand3cm/hrespectively.Findtherateofchangeofitsvolumewhenitsdiameterandheightare2mand13mrespectively.點選【上一頁】回到網上教室Click【LastPage】toGoBack