ADDITIONAL MATHEMATICSPROJECT WORK TASK 2 / 2014 Name: Class: 5 Jati Teacher: Encik Amir Arif bin Mohd Nasir CONTENTS NO. TOPICS PAGE 1. Title 2. Acknowledgement 3. History o !o!corn ". O#$ecti%es &. Section A '. Section ( ). Concl*sion +. ,*#ric TITLE APPLICATION OF MATEMATIC! IN POPCO"N PAC#A$IN$ AC#NO%LE&$EMENT -irst o .ll/ I wo*ld like to e0!ress my gr.tit*de to my .ddition.l m.t1em.tics te.c1er/ Encik Amir w1o 1.d 1el!ed me . lot t1ro*g1o*t t1is !ro$ect work. 2it1o*t 1is g*ide/ I m.y not 1.%e com!leted t1is !ro$ect. Secondly/ I wo*ld like to t1.nk my !.rents or !ro%iding e%eryt1ing s*c1 .s money to #*y e%eryt1ing w1ic1 .re re3*ired to com!lete t1is !ro$ect work .s well .s t1eir .d%ices/ w1ic1 is essenti.l in t1e !rogress o doing t1is !ro$ect work. I .m gr.te*l or t1eir const.nt s*!!ort .nd 1el!. I wo*ld .lso like to t1.nk my riends w1o 1.%e contri#*ted lots o ide. on 1el!ing me to cre.te .n .!!ro!ri.te title .s well .s gi%ing t1eir comments on my rese.rc1. I re.lly .!!reci.te t1eir kindness .nd 1el!. I wo*ld like to e0!ress my .!!reci.tion to t1ose w1o .re in%ol%ed eit1er directly or indirectly in 1el!ing me to com!lete t1is !ro$ect work. T1.nk yo* or .ll t1e coo!er.tion gi%en. I!TO"' OF POPCO"N Po!corn w.s irst disco%ered t1o*s.nds o ye.rs .go #y N.ti%e Americ.ns. It is one o t1e oldest orms o corn4 e%idence o !o!corn rom 3'55 (.C. w.s o*nd in New 6e0ico .nd e%ene.rlier e%idence d.ting to !er1.!s .s e.rly .s ")55 (.C. w.s o*nd in Per*. Some Po!corn 1.s #een o*nd in e.rly 1755s to #e . !*r!le color. T1e Englis1 w1o c.me to Americ. in t1e 1't1 .nd 1)t1 cent*ries le.rned .#o*t !o!corn rom t1e N.ti%e Americ.ns. 8*ring t1e Gre.t 8e!ression/ !o!corn w.s com!.r.ti%ely c1e.! .t &915 cents . #.g .nd #ec.me !o!*l.r. T1*s/ w1ile ot1er #*sinesses .iled/ t1e !o!corn #*siness t1ri%ed .nd #ec.me . so*rce o income or m.ny str*ggling .rmers. 8*ring 2orld 2.r II/ s*g.r r.tions diminis1ed c.ndy !rod*ction/ c.*sing Americ.ns to e.t t1ree times .s m*c1 !o!corn t1.n t1ey 1.d #eore. At le.st si0 loc.lities :.ll in t1e 6idwestern ;nited St.tes< cl.im to #e t1e =Po!corn C.!it.l o t1e 2orld= 4 ,idgw.y/ Illinois> ?.l!.r.iso/ Indi.n.> ?.n (*ren/ Indi.n.> Sc1.ller/ Iow.> 6.rion/ O1io> .nd Nort1 @o*!/ Ne#r.sk.. According to t1e ;S8A/ most o t1e corn *sed or !o!corn !rod*ction is s!eciic.lly !l.nted or t1is !*r!ose> most is grown in Ne#r.sk. .nd Indi.n./ wit1 incre.sing .re. in Te0.s. As t1e res*lt o .n element.ry sc1ool !ro$ect/ !o!corn #ec.me t1e oici.l st.te sn.ck ood o Illinois/ ;.S.A. O(JECTI)E! A!!ly .nd .d.!t . %.riety o !ro#lem9sol%ing str.tegies to sol%e ro*tine .nd non9ro*tine !ro#lems. Ac3*ire eecti%e m.t1em.tic.l comm*nic.tion t1ro*g1 or.l .nd writing/ .nd to *se t1e l.ng*.ge o m.t1em.tics to e0!ress m.t1em.tic.l ide.s correctly .nd !recisely. Incre.se interest .nd conidence .s well .s en1.nce .c3*isition o m.t1em.tic.l knowledge .nd skills t1.t .re *se*l or c.reer .nd *t*re *ndert.kings. ,e.liAe t1.t m.t1em.tics is .n im!ort.nt .nd !ower*l tool in sol%ing re.l9lie !ro#lems .nd 1ence de%elo! !ositi%e .ttit*de tow.rds m.t1em.tics. Tr.in st*dents not only to #e inde!endent le.rners #*t .lso coll.#or.te/ to coo!er.te/ .nd to s1.re knowledge in .n eng.ging .nd 1e.lt1y en%ironment. ;se tec1nology es!eci.lly t1e ICT .!!ro!ri.tely .nd eecti%ely. Tr.in st*dents to .!!reci.te t1e intrinsic %.l*es o m.t1em.tics .nd to #ecome more cre.ti%e .nd inno%.ti%e. ,e.lise t1e im!ort.nce .nd t1e #e.*ty o m.t1em.tics. !ECTION A 1< -or t1is .cti%ity yo* will #e com!.ring t1e %ol*me o 2 cylinders cre.ted *sing t1e s.me s1eet o !.!er. Bo* will #e determining w1ic1 dimension c.n 1old more !o!corn. To do t1is/ yo* will 1.%e to ind . !.ttern or t1e dimensions or cont.iners. 6.teri.ls4 • +.&011 in. w1ite !.!er • +.&011 in. colored !.!er • T.!e • Po!corn • Pl.te • C*! • ,*ler .. T.ke t1e w1ite !.!er .nd roll it *! .long t1e longest side to orm . #.seless cylinder t1.t is t.ll .nd n.rrow. 8o not o%erl.! t1e sides. T.!e .long t1e edges. 6e.s*re t1e dimensions wit1 . r*ler .nd record yo*r d.t. #elow .nd on t1e cylinder. @.#el it Cylinder A. +.&C 11C #. T.ke t1e colored !.!er .nd roll it *! .long t1e s1orter side to orm . #.seless cylinder t1.t is s1ort .nd sto*t. 8o not o%erl.! t1e sides. T.!e .long t1e edge. 6e.s*re t1e 1eig1t .nd di.meter wit1 . r*ler .nd record yo*r d.t. #elow .nd on t1e cylinder. @.#el it Cylinder (. 11C +.&C 8I6ENSION CB@IN8E, A CB@IN8E, ( HEIGHT 11C +.&C 8IA6ETE, 2.'C 3."C ,A8I;S 1.3C 1.)C 2. 8o yo* t1ink t1e two cylinders will 1old t1e s.me .mo*ntD 8o yo* t1ink one will 1old more t1.n t1e ot1erD 21ic1 oneD 21yD T1e two cylinders will 1old t1e dierent .mo*nt. Cylinder ( will 1old more t1.n Cylinder A. T1is is #ec.*se t1e r.di*s o Cylinder ( is longer .nd t1is m.kes t1e %ol*me o it more t1.n Cylinder A. Alt1o*g1 t1e 1eig1t o Cylinder ( is s1orter t1.n Cylinder A/ 1owe%er t1is does not .ect m*c1 com!.red to t1e eect o dierence in r.di*s. 3. Pl.ce Cylinder ( on t1e !.!er !l.te wit1 Cylinder A inside it. ;se yo*r c*! to !o*r !o!corn into Cylinder A *ntil it is *ll. C.re*lly/ lit Cylinder A so t1.t t1e !o!corn .lls into Cylinder (. 8escri#e w1.t 1.!!ened. Is Cylinder ( *ll/ not *ll/ or o%erlowingD Cylinder ( is not *ll. T1ere is still s!.ce in t1e cylinder or more !o!corn. As yo* s1.re yo*r !o!corn sn.ck/ .nswer t1e 3*estions #elow. ". .< 2.s yo*r !rediction correctD How do yo* knowD Bes/ t1e !rediction is correct. It is #.sed on t1e orm*l./ t1e %ol*me o t1e cylinder is e3*.l to ErF1. According to t1e orm*l./ r.di*s r 1.s more eect t1.n 1eig1t/ 1 since r.di*s/ r is s3*.red. T1*s/ Cylinder ( 1.s . gre.ter r.di*s .s well .s . gre.ter %ol*me com!.red to Cylinder A. #< I yo*r !rediction w.s incorrect/ descri#e w1.t .ct*.lly 1.!!ened. Cylinder ( 1.s . gre.ter %ol*me t1.n Cylinder A. &. .< St.te t1e orm*l. or inding t1e %ol*me o . cylinder. V = πr²h #< C.lc*l.te t1e %ol*me o Cylinder AD V = πr²h = π x 1.3² x 11 = 58.4 inch³ c< C.lc*l.te t1e %ol*me o Cylinder (D V = πr²h = π x 1.7² x 8.5 = 77.2 inch³ d< E0!l.in w1y t1e cylinders do or do not 1old t1e s.me .mo*nt. ;se t1e orm*l. or t1e %ol*me o . cylinder to g*ide yo*r e0!l.in.tion. T1e cylinders 1.%e dierent r.di*s .nd 1eig1ts. T1ereore/ t1e %ol*mes .re dierent. &ATA COLLECTION T1e cylinder wit1 . gre.ter r.di*s .nd di.meter will 1.%e . gre.ter %ol*me. T1e r.di*s o Cylinder ( is gre.ter t1.n t1e r.di*s o Cylinder A. T1e %ol*me o Cylinder ( is gre.ter t1.n t1e %ol*me o Cylinder A. T1ereore/ Cylinder ( is .#le to 1old more !o!corns com!.red to Cylinder A. 8I6ENSION CB@IN8E, A CB@IN8E, ( HEIGHT :inc1F< 11 +.& 8IA6ETE, :inc1F< 2.' 3." ,A8I;S :inc1F< 1.3 1.) ?O@;6E :inc1G< &+." )).2 '. 21ic1 me.s*rement im!.cts t1e %ol*me more4 t1e r.di*s or t1e 1eig1tD 2ork t1ro*g1 t1e e0.m!le #elow to 1el! yo* .nswer t1e 3*estion. Ass*me t1.t yo* 1.%e . cylinder wit1 . r.di*s o 3 inc1es .nd . 1eig1t o 15 inc1es. Incre.se t1e r.di*s #y 1 inc1 .nd determine t1e new %ol*me. T1en *sing t1e origin.l r.di*s/ incre.se t1e 1eig1t #y 1 inc1 .nd determine t1e new %ol*me. CB@IN8E, ,A8I;S HEIGHT ?O@;6E O,IGINA@ 3 15 282.7 INC,EASE8 ,A8I;S 4 10 502.7 INC,EASE8 HEIGHT 3 11 311 21ic1 incre.sed dimension 1.d . l.rger im!.ct on t1e %ol*me o t1e cylinderD 21y do yo* t1ink t1is is tr*eD Incre.sing its r.di*s 1.d . l.rger im!.ct on t1e %ol*me o t1e cylinder com!.red to incre.sing its 1eig1t. T1is is #ec.*se t1e r.di*s is s3*.red to ind t1e %ol*me/ w1ic1 incre.ses its im!.ct on t1e %ol*me. !ECTION ( QUESTION I yo* were #*ying !o!corn .t t1e mo%ie t1e.ter .nd w.nted t1e most !o!corn/ w1.t ty!e o cont.iner wo*ld yo* look orD Cl*e 4 Bo* need more t1.n one ty!e o cont.iners. Bo* .re gi%en 355 cmF o t1in s1eet m.teri.l. E0!l.in t1e det.ils. ANSWER 1. Cylind! C"n#$in! % "&nd #"& Surface Area = 2πrh + πrF H 355 Volume = πr²h H πrF : h = 300 πr² 2 πr 300 πr² 2 πr < ?ol*me H &'3.'2 2. C'( C"n#$in! * "&nd #"& S*r.ce Are. H lF I "lF H 355cmF & lF H 355 lF H '5 l H ).)&cm ?ol*me H lG H :).)&<G H "'&."+ cmG