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suRFAcE^?ii: Af;DVoLUMES1' Howmanyballs,eachof radius1cm,canbe made rom a solidsphereof leadofradius8cm? Ans.512]2' A-solid phereof radius3cm s meltedand hencast ntosmallsphericalballseachof diameter0.6cm.Find he numberof smallbails hus obtained. A";. ;;;odf -"""3' A solidmetallicsphereof diamete 21cm s meltedand recasted nto a numberofsmallercones'eachof diameter7cmandheight3cm.Find he numberof conessoformed.[Ans.126J4' A cone s 8.4cmhighand he radiusof its base s 2.1cm. t is meltedand recast ntoa sphere.Find he radiusof the sphere.[Ans.2.1cm]5' A solidrectangularblockof metal49cmby 44cmby lgcm is meltedand ormed ntosolidsphere. alculate he radiusof solidiphere.t,qnr. r"rnt-6' Thediameterof a sphere s42cm. t is meltedand rawn intoa cylindricalwireof28mmdiameter.Find he lengthof the *ir".t An". Ogrl7. Thebase adiusand heightof a rightcircularsolidcone are 2cmandgcmrespectively.t is meltedandrecalt intospher"" otdiameter2cmeach.Find he_ numberof spheresso formed. Ans.gJ8' A cylindricalbucket28cm n diameterand72cmhigh sfull of water.Thewater semptied ntoa rectangular ank 66_cmong,and28cmwide.Find he heightof thewater evel n the tank. Ans.24cml9' A cytrindricalontainer s filledwith ce-cream,whose adius s 6cm and height s1Scm. hewhole ce-creams distributedo 10children n equal"on"" havinghemisphericalops. f lhe heightof the conicalportion s4 times he radiusof thebase, indthe radiusof the ice-cream one.[Ans.3cm]10'4 rightcircular.cylindelfravingdiameter21Lmand hight Bgcm sfu1of ice-cream.The ce-creams to be filled n conesof height 2cmand diameter7cmhavingahemispherical hapeon he top. Find he numberof suchconeswhichcan be illedwith ce-cream.[Ans.54]11.Howman-y pherical eadshots each4,2cm n diametercan be obtained romarectangular olidof leadwith dimensions 6cm, 42cmand21cm. Taken= 22t71.[Ans. ,500J - ' . ' - - -12.A spherical annonball,28cm n diameters rnelted ndcast ntoa rightcircularconicalmould, he baseof which s 35cm n diameter.Find he height-ot re cone,correct o oneplaceof decimal.[Ans.3S.g4 m]13.A vessel, n the form of a hemispherical owl, s full of water. ts contentsareemptied n a rigtrtcircularcylinder.The nternal adiiof the bowland he cylinderare3.5cmand 7cmrespectively. ind he height o whichwaterwill rise n thecyf nder. Ans. l12cml14.Ahemisphericalowlof internal iameter 8cmcontains iquid.This iquid s o befilled n cylindricalbottlesof diameter3cm andheight4cm. tto* r"nyl"t1"" "r"equired o empty he bowl? Ans.54]

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15'Agirlfl l lsa cylindrical ucket32cm n height nd gcm in radiuswithsand.Sheempties he bucketon groundandmakesi conicatheap"f ih;;;1. ffthe heightofthe conicalheap s 24cm, ind (i) he radius;""Jiiil the slantheightof the heap.lAns. 43.27cml16 'Therainwater rom a roof 22mx 20mdrains ntoa conicalvesselhavingdiameterof baseas 2m and height3.5m. f thevessel " ir"i tuu, ind the rainiatt incm). Ans.1/3mml17'Asphericalshellofead,whoseexternaldiameters 18cm, s meltedandrecast ntoa rightcircularcylinder,whoseheight s 8cm"nJ ai"r"ter 12cm.Determineheinternaldiameterof the shell.18.A ollow etallic.vlindricaltubeas n nternatradiuscm ndn",!ti;iIl]ffTlthicknessof the tube s 0.5cm.The ube s metteJandcast ntoa rightcircularconeof height7cm.Find he radiusof the cone. An"lS.+ mt19'what is the leastnumberof solid.metallic pheresof 6cm n diameter hatshouldbemeltedand recast o form a solidmetalcytinoerwhoseheight s 4scm anddiameter4cm. Ans.S]20'A cylinderwhoseheight s equal o its diameterhas he samevolumeas a spheresof radius4cm.calculate he iadiusof the baseof he cylindercorrect o one^ decimal lace.[Ans.8.5cm]21'Eightmetallicsphereseactr'of adius2mmare meltedandcast ntoa singlesphere.calculate he radiusof the newsingre phere.tAn".4mml - -l22'Theradiusof a sphere s 9cm. t is meltedano rawn intoa wire of diameter2mm.^^ IinO he engthoJthewire.[Ans.97,200 m]23'Thediametersof the internll and external urfacesof a hollowsphericalshellare6cmand 1Ocm espectively.f it is meltedandrecast ntoa solidcylinderof height2213 m, ind the diameterof the cylinder. Taken = z2tr). Ans.14 ;i24'The otalsurfaceareaof a right rcular.cylinder is osr 2cm2and he circumferenceof its base s 88cm.Find he vofumeof lie cyrindei.

[Ans.36,960cmsJ25'Determinehe ratioof the volumeof a cube o that of a spherewhichwilfexacily itinside hecube. Ans.6 : nJ -' -r"-'26 'The argest.spheres carvedout of a cubeof side7cm.Find he volumeof the_ sphere. Take = 22l7l. Ans.1Z9.6T u cm]27'Find he depthof a cylindrical ankof radiui 2Bm, f its capacity s equal o that of arectangularankof size2gmx 16mx 11m. Ans. mJ - - -' '28 'A rectangular ank.15mongand 1.1m-gr.oais iequireo o receiveentire iquidcontents rom a full cylindrical ankof internaldiameter21mand engthsrn.Find^^ the leastheightof the tank hatwiil serve trepurpose.[Ans.10.s t-29'Thesurfaceareaof a solidmetallicsphere s iis'o sq cm. lt is meltedandrecastinto..solidightcircularconesof radius2.Scmandheightgcm.carcuiate:(i) The radiusof the solidsphere;

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(i i) Thenumberof cones ecast. Take = 8.141.[Ans. a) 1Ocm,b)80]

TYPE B1'' 35:Tn:s throusha (cvlindrical) ipeof internatdiameter7cmat 5m/sec.(a) Thevorume n ritresorw{ql dischargedby pipe n oneminute;(b) The ime aken n minutes, he pipe,"iJJt"fe to fifl an empty ectangulartank,4m x 3my Z.S1m.Ans.(ai .tSScu ,, (O)24 min!2' water flowsalonga pipeof radiusO.bm t acmtsec,Jfrispipe s draining le waterrom a tankwhichholds1,000 itresof waterwtren ull.How ongwould t take o^ ggTplgtelyempty he tank? Ans.30.7 ours] 'Y'|r' vv ' 'v'!r,wv3' water is beingpumpedout througl a circuL'rpipewhoseexternaldiameter s 7cm.f the rowof *{gl is 72cmper second,how,;t ritresot*ui"i ",[ o"ing pumpedout n onehour? Ans.9979.2itresl ' '--"'4' A rectangular ank.15m ongan! rj r- |..o"d is required o receiveentire iguidcontents rom a full cylindriial tankof internaloL-lneter 1mand ength5m.Findthe feastheightof the tank hat will serve d ilrp.se. (Taken = 22ltl.[Ans.1o.bmJ5' water in a canal,30dmwideand] 2m deep . hoviingwith a velocityof 1gkmper ,hour'Howmuch".1"" j! it rrigaten30minui"",r6"r .i"i""ai"6 waters_ requiredor irrigation?[Ans.z.-b q kmJ ' --- ' '6' A hemisphericalank ui l of water s'emptieo y a pipeat the rateof 3 4/7 itrespersecond'Howmuch ime t will take o half"rpiv tt" tank, f the tank s 3 metres niameter?[Ans.1 .SminJ7 water is flowingat the rateof Skmper hour hrougha pipeof diamete l4cminto aectangular ankwhich s 50m ongand44mwide]Determinehe time n which heevelof water n the tank will riseby 7cm. Ans 2hrJ8' A poolhasa uniformcircular "to""l-"""iil;i;ius sm and uniformaeptl 1.4m. ts filledby a pipewhichdeliverswaterat the rate of 20 itresper second.calculatein minutes he time aken o fillthepool. lf the pooii" emptied ; iiminutes uynothercylindricalpipe hroughwhichwaternows4 the rateof 2m per second,calculate he radiusof the pipe n cm. [Ans.g 1A3 m]1.2.

Awellwith10mnside iameter'.li!51f d"."qEarthaken utof t sspreadrloundoawidth f5m o ormanemdanrrment.'iinot " t,"igr,t f heembankment.[Ans.14/3 m] rrervrrL r ' ' r Lrre sf rEarth akenout of digginga circular ankof diameter l7.1m,isspreadall aroundthe tankuniformly o awidth of 4m, o forman embankment f height2m.calculatethe depthof the circurar ank correcl !9 tryod;i;;i;iaces. (Thedepthof the tanks uniformeverywhere).[Ans.h = 2.246m] - "-' r

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3. A well28.8m deepandof diameter?r.i:9rg ,p. Thesoirdugup s spreadarlaround he wellto makea platform1m highJonsioeringhe fact loosesoilsetiles oa height n the ratio6 : s. Find he widthoitt " pt"tror,n.[Ans.r = 4cmJ4' An agricultural ield s in the form.ofa rectangieoi lengttt20mandwidth 14m.A10mdeepwell of diameter7m s dug n " "o.i"i ot " ri"lo and he "iliii"';t "i'outf the well s spreadevenlyover hJremainingp"rt or he field.Find he rise n itslevel. Ans.1.6m]5' An opencylindricalvesselof internaldiameter7cmandheightgcmstandson ahot'izontalable. nside his solidmetallic ighi ciicular cone, he diameterof whosebase s 3'5cmandheight8cm.Find he volime of water required o fill the vessel. fthe cone s replacedby anotherconewhose reigtrts 1 sAcmand he radiusofwhosebase s 2cm, ind the drop n.water "u"i. [en" .1or21cml6' A cylindrical.can hosebase shorizontatanooiiadius 3.scmcontainssilfficientwaterso thatwhena s.pheres placed n thecan, he water ust covers he sphere.Given hat the sphere ust fits into he ""n, c"tcui"t",(a) The otal surfaceareaof the can n contaciwith waterwhen he sphere s init :(b) Thedepthof water n the can before he spherewasput into he can.Giveyouransweras proper raction.7.Avessers n heormra nvertedl*"; rts eit#:J3ll,l3,ffl""hllf ?',i"i:i*!t!"lt fsopen s Scm. ts is filledwithwaterup tJrim. when leadshots,eachofwhich s a sphereof radius0.5cm,aredroppiro "t " the vessel,one ourthof thewateroverflows, ind the numberof lead"hb.tg ropped nto he vessel.[Ans.100J' An invertedconicalvesselof radius6cmandh"ig-rit cm is completely illedwithwater'A sphere s lowered nto he waterand tsfize is such hatwhen t touchesthe sides t is ust immersed.Whatfractionof watei over-flows?[Ans.3/g19' A vessel n the shapeof a cuboidcontainssomewater. f three dentical pheresare mmersedn the water, the levelof the water ncreasesuv zcm. l the areaofbaseof cuboid " 1j,9:1.:m and ts height s rzcrn, determine he radiusof thespheres. Ans. = s{290/11cm]TYPE D1' A solidconeof height12cmandbase adiusGcmhas he top 4cm removedas;Hyi3:he risure.indhewhoreurrace";; o;iil;;;"1il';il";;":ion".350.7 q cml oI12a'^J2. I*:ii::1,?jgllJi:*ftr ra*-le are 9_", nd rcmandtssranteishts

ftl t9 t-viI\u

1Ocm.Find ts total surface area. [Ans. Z4lgnsq cm]

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3. A containermadeup of a metalsheei s in the form of a frustumof a coneof height16cmwith radiiof its upperand owerendsas 8cmand20cm "rp""tir"ly. Find hecostof milkwhich.can ompletelyill the contain"t "i ttt" rate oi gs,i 6 p" r litreandthe costof the metalsheetused, f t costsRs.sper 100sq cm. (use n= 3.141.[Ans.Rs.150.721A ent s n he orl-or :.vri.n99lol,Llt"f"i 4.2mand eisht m,surmountedyaconeof equalbaseand height2.8m.Find he capaciiyof the tent and he costof thecanvasat Rs.100 er squaremetre. Ans.Rs.7,S-gO]In he adjoining igurg,a hemisphere f radius'5cm urmounted y a right circularconeof base adiusScm.Find he volumeof solid f the heightof tire"o"n"is 7cm.Giveyour answercorrect to two placesof decimal. Ans. ds.zq", "r j

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A buoy s made n the form of a hemisphere urmounted y a right conewhosecircularbasecoincidgswith the planesurfaceof hemisph-ere.he radiusof thebaseof the cone s 3.5metresand tsvolume s two-thir.ds f the i.ri"pfr"r".calculate the heightof the coneandthe surfacearea of the buoy"ori"ft to twoplacesof decimal.Ans.141.17q m]A solid oy is in the.formof a himispheresurmounted y a right circularcone. f theheightof the cone s 4cm anddiameterof the base s 6Cm, ilculate:(a) the volumeof the toy,(b) surfaceare.a f the toy (usen = 3.14). Ans. a)94.2cu cm, (b)109.62 q cm]A circus ent is in !h.e !"p" of a cylindersurriounteouya cone.Thedianreter fthe cylindricalpart is 24mand ts height s 11m. f th; vertexof the tent is 16mabove he ground, ind the areaof canvas equired o make he tent. Ans.1320 qmlIn he adjoining igure,modelof a rocket,which s drawn o a scaleof 1 : 1S00,calculate:(a) the totalsurfacearea n r sq m.(b) the volumeof the rocket n cu m. [Ans.1g,g00n g ffi,3,44,250ncumJ