Page 94 - MATHEMATICS COURSE FOR SECONDARY SCHOOLS BOOK 2

of the circular table,
14 cm
And the area of the minor sector
5. 31 How long is the hem of a circular table-
6.
so Rebecca took it to
the joiner to change its shape. She asked him to change the table top to
a square with the maximum possible area. Can
4.
A firm makes Rubik c2u95b8es of side 6 cm and sells 4t.hem in sets of 12. The firm wants
to design a rectangular cardboard box to
2. 9. 2.
8. A watch is readi8n.gA04w:3a0tch.iTs hreardaidnigus04o:f3t0heh. The radius of the 8. Acirwclaetcfhorims irnegaCdtihanlecguf0alac4te:e3o0tfhheth. aeTrhecaleoorcafkdtihsues1m.o2fincthomer.sector defined
2.
by the time. the circle forming the face of the clock
5 28.8 cm2 22 cloth if its diameter is 10.7 m? Use 􏰀 = ––.
11.you help the joiner to work out what to do? 3 Rubik-volume
O
So the area of the major sector 7 5 (201.1 2 28.8) cm2
32 The circumference of a circle is 176 cm. 2 22
5 172.3 cm –– AndFthine daretaheofrtahde imuisnorfsetchtoercircle. Use 􏰀 = . 4.
7
33 Statedtehfineedhibgyheeacrhteswminpgeirsa1t7u2r.e3 cinm e. ach pair. 5 28.8 cm
And the area of theAmndintohresaercetaorof the minor sector 4. And the arHeaenocfet2thheemairneoarosfetchteormajor sector of the circ4le.
5 28.8 cm
22
5 28.8 cm 2 5 28.8 cm 2
So the area of the major sector
7S.othearTheaeofctihrecumSmoajtfohererseaenrcetcaoerooffthaecmiracjolersisec3to0r8cm. holdasetofRubikcubes.Thefirmwants
So the area of the major sec2tor O
(a5) 2(250°1C.1, 232°8C.8) cm (b) 8°C, –9°C
5 F(2i0n1d.1th2e2d8i.8a)mc5met(e2r021o.f1t2he2c8i.8rc) lcem. Use π= 5 (201.1 2228.8) cm
5 172.3 cm
(a) the minor sector
(b) th(eb)majortshecetomr.ajorarc
CalculatetheareaoCfatlhceulmatientohresaercetoarodfetfhienemdinorsectordefined Calculate the area of the minor sector defined
(b) the major secto(rb.) the major sector.
bythetime. bythetime.
15. A watch is reading 04:30 h. The radius of
(b) the major sector. O 2.
by the time. by the time.
8. Awatchis9re.aAdinragd0iu4s:3o0fha.cTirhcelerawdiituhscoefnthreOis10cm.
22OO
2 2
5 172.3 cm 2 5 172E.3xcemrcise 18c
7
The diagra2m958above shows2a95c8ircle of radius 9.4 cm are the designer. Suggest a suitable way to
(c) –5°F, 2°F (d) –7°F, –8°F
2958 witphaacksetcThthoerdRaiuangbgrialkemocafub2obv7ee5sso,h.ioEnwvosarlaudcaeitrrceltetohoefsaratrdiesiuafysotfhthee
sector. 9.4 cm with a sector angle of 295°. Evaluate conditions.
the area of the sector.
5 172.3 cm
Hence the area of the major sector of the circle
Hence the area of tHhenmcaejtohresaercetoarooffththedem=cai9rjco8lrecsemct.or of the circle Hdefnincedthbeyaeraecahosfwthinegmisaj1o7r2s.e3cctomr2o. f the circle
1.
to use as liOttle cardboard as possible. You 2958
Fig. 18.21 Sector of a circle
22 defined3b4y eUacshe stwhdienefgdiniisead1g7br2ya.m3eacmoh ns.wp2inagies 317020.3tcomc.onvert:
defined by each swing is 172.3 cm .
In the following questions
8.
1. 1.
354
Use π as 3.14
Fig. 18.21 Sector oFfiga. c1i8rc.2le1 Sector of a circle c
9.4 cm withriasnegctloe9rs.4aancsgmlpewoifsths2i9ab5sl°e.c,Etovralaunagtlee of 295°. Evaluate 9th.4e acrmeawoifththsaebscseyetcocettoarorcrdh.aensfigwlneineogdff2rbo9my5°e.AaEtcvohaBlus.wateing from A to B.
1.
O
OOO
The diagraDmrabwovaeTsshhmeodwainsagayracmircalebovferasdhiouws s a circle of radius 125 cm. determine the area of the minor T9.h4ecdmiawgriathmaaDsbeoecvtteorrmshainongwelsethaoefcai2r9eca5le°o.ofEfthvraedlmuiuaistneor sector defined
(a) 35°C to °F (b) 85°C to °F
1.
12.4 TArip-menadtuilucm swings from A to B through
Exercise 18c
Fig. 18.21 Sector of a circle
Exercise 18cExercise 18c
(c) 86°FEtxoe°rCcise 18c (d) 140°F to °C.
a
an angle of 75o. The lengthhof the string is
Fig. 18.18 Circle
aDnegtleermofin8e5t°h. eT8ah3reecalmeon. fgDtheteoemrfmtihnienoerstsrheinecgtaoriresda1eo2ff5intcehmde .sector
defined
Fig. 18.18 Circle
Fig. 18.18 Circle Fig. 18.18 Circle
6. Aanpgelendouf l1u4m7°s.wcTiirhncegleslefonrorgmthinPogfttohQe fstathrcirenoguogfishthaenclock is 12.8 cm. angle of 147°. Thealnegnlgethofof14th7e°.sTtrhinegleisngth of the string is
O
angle of 85°. Thaenlaeanggltehleofof 8fth51e°5.s0Ttrohi.negThleisneg1lt2he5nocgfmth.eosftrtinhgeist1r2in5gcmis.
(a) the minor sector
a8n3gclme o. fD1e4te7r°m.CTianhleceutlhleaentegartthehaeoofafrthethaeeostsfreitcnhtgeorimsdienfoinr esdector defined
83 cm.1D4.etermiAnect8hl3oecamkre.iasDorefetetahrdmeisinegectto0hr3ed:a0er0feinaheo.dfThthesreacdtoirudseofifned
Fig. 18.18 Circle (b) the major sector.
The diagram above shows a circle of radius
8b3y cemac.hDsewteinrmgbifynroethmtehPetimatoreQ.a .of the sector defined
The diagram above shows a circle of radius 9.4 cm
Fig. 18.21 Sector of a circle
5. A pendulum swings from A to B through an
The diagram aabnogvle sohfo8w5s°.aTchireclenogfthraodfiuths e string is
125 cm.
on graph paper, with
b
the area of the secttohre. area of the sector.
the area of the sector.
5. A pendulum6. sAwipnegnsdfurolumAswtoinBgsthfrroumghPatno Q through an
a fixed perimeter of 24 cm. Name the sides of
5. Apend1u3lu.mswA5in.gpAsefpnroednmudluAulumtomBswthirnogusgsfhfroraomnmAPtotBotQhrotuhgrhoaungh 5. Aanpgelendouf l8u5m°.sTwahniegnlglesnofgfrot1hm4o7Af°.tthToehBsettrlhienrnogutighs h1o2af 5nthcems.tring is
The diagram above shows a circle of radius
by each swing frombyAetaochB.swing from A to B.
by each swing from A to B. 9.4 cm with a sector angle of 80.7°. Calculate
the area of:
6. A pendulum7.sAwicnlgosckfroismrePadtoinQg 0th3r:0o0ughh. Tanhe radius of the 6. A pendulum sw6in.gAs fproenmduPlutomQswthinrogusgfhroamn P to Q through an
byeachswingftrhoembcyPiertacoclehQf.sowrimngifnrogmthPetfoaQce.oftheclockis The diagram aboveTshheodwisagaracmircalebovferasdhiouwss a circle of radiusby each swing from P to Q.
T9.h4ecdmiawgriathmaasbeocvteorshanogwlse aofci8r0c.l7e°o. fCraldciulsate
with a sector2a. ngle of 80o. Calculate the length of:7. A clock is r8e.adAinwga0tc3h:0i0s hre.aTdhinegra0d4i:u3s0ohf.tThehe radius of the
a8r1eaDcomeftet.hrDme mientienrtohmresiaenrcetoatrohdfetfhaienremdainoofr tsheectosrecdteofirned Dbyetearcmhinswe itnhge afroema oAf thoeBm. inor sector defined
Determine the
by each swing from P to Q.
defined by each swing from P to Q.
9.4 cm with a secto9r.4ancgmlewoifth80a.7se°.ctCoarlacnuglaleteof 80.7°. Calculate
14.8 cm. Calculate the area of the minor
9th.4e acrmeawoift:h a sector angle of 80.7°. Calculate
7. A clock is readi7n.g A03c:0lo0chk.iTs hreardaidnigus03o:f0t0heh. The radius of the 7. Acircloecfkorismrienagdctihnrceglef0a3fco:e0rm0ofihnt.hgTethcelorfcakdcieiusso1fo2tf.h8tehcecmlo.ck is 1.2 cm.
the area of: the area of: the area of:
sector defined by the time.
(a) th(ea)minor tshecetomr inor arc
(a) theminorsecto(ra) theminorsector
circle forming the fcaircceleofothrme icnlogctkheisfa1c2e.8ocfmth.e clock is 12.8 cm. cCiarclcleulfaotremthinegatrheae ofafcteheofmthineocrloseccktoisr 1d2ef.8incemd .
Determine the area of the major sector defined
Fig. 18.19 Sector of a circle
is 1.5cm. Determine the area of the major
Fig. 18.19 Sector of a circle
9. ACarlacduiluasteotfhaecacailrnrcecgualeloawfotfteiht2het9hcm0e°in.natorereaOseocistfo1trh0decemfmin.eindor sector
15.8 cm with a sector angle of 49.5°. Calculate
O
by the time.
9. A ra1d6i.us of aAcaireacaldeoiwuf stihthoefcmeanacjtoriercOsleecistwo1ri0tdhcemfcin.eendtbrey aOseisct1or5cm.
circle forming the fcaircceleofothrme icnlogctkheisfa1c.2e comf t.he clock is 1.2 cm. cDirectelermfoinrme itnhgebtayhreaafsaoecfettohorefatmnhgealjecolrosfcek7c5tios°r.1d.2efcimne.d
DeterminetheareaDoeftethrmeminaejothreseacretoarodfetfhineemdajorsectordefined The diagram above shows a circle of radius Dbyetehremtinmeet.he area of the major sector defined
sector defined by the time.
10. The radius of a circle O is 15 cm. Evaluate the by the time. by the time.
the area of the secOtor.
O O 9. A radius of a cir9c.leAwriathdicuesnotrfeaOciirscl1e0wcimth. centre O is 10 cm.
CalculatetheareaoCfatlhceulmatientohresaercetoarodfetfhienemdinorsectordefined Fig.Th18e.1d9iaSgercatomr oFafibga.oc1vi8rec.1lse9hoSwecstoar coifraclceirocfleradius 15.8 cm Cbyalacusleactteorthaenagrleaoof f7t5h°e. minor sector defined
3.
defined by a sector angle of 80o.
Fig. 18.19 Sector of a circle
11.
by a sector angle obf y75a°s. ector angle of 75°. with a sector angle of 49.5o. Calculate the length of by a sector angle of 75°.
The diagram above shows a circle of radius
The diagram aboveTshheodwisagaracmircalebovferasdhiouwss a circle of ra1d0i.usThe radius of a circle O is 15 cm. Evaluate the
the arc.
3. 3. 3.
3.
11. 11.11.
38.58 38.58 38.58
angle of 290s°e. ctor angle of 290o.
T15h.e8dcimagwraimthabsoevcetosrhoanwgslea ocfir4c9le.5o°f. rCaadlicuuslate
10. The ra1di7u.s of a1Th0ci.rceTlehreaOdraisdui1su5socofmfaa. cEciivraclueaOte itsihs1e255cmcm. E.vEalvualtue athte 15.8 cm with a sec1to5r.8ancgmlewoifth49a.5se°.ctCoar lacnuglaleteof 49.5°. C1a0l.cuTalrahetea roafdtihues mofaajocrirscelcetoOr dise1fi5necdmb. yEavasleucattoer the
1th5e.8arcema owfitheasseeccttoorr. angle of 49.5°. Calculate
area of the majotrhseeacraetroaeroadfoetfhfinetehmdeabjmyorasjseoecrctotsorerdcetfoinredebfiynaesdecbtoyra arnegaleofofth2e9m0°a.jor sector defined by a sector
the area of the secttohre. area of the sector. 10.the area of the sector.
angle of 290°. angle of 290°.
O
38.58
OOO O
11.
O
18.
Fig. 18.20 Sector of a circle
O
Fig. 18.22 Sector of a circle
O
The diagram above shows a circle of radius 10.5 cm with a sector angle of 1.7 radians. Calculate the area of the minor sector.
Fig. 18.20 Sector of a circle
38.58
The diagram above shows a circle of radius
O
O
18.3 cm with a sector angle of 38.5°. Calculate:
(a) the area of the minor sector
The diagram above shows a circle of radius 18.3 cm
(b) the area of the major sector.
with a sectorFaign.g1l8e.2o0f 3S8ec.5toor. Cofaalcuirlcaltee: Fig. 18.20 Sector of a circle
Fig. 18.20 Sector of a circle Fig. 18.22 Sector of a circle
The diagram above shows a circle of radius
The diagram above shows a circle of radius
The diagram aboveTshheodwisagaracmircalebovferasdhiouwss a circle of radius
T18h.e3dcimagwraimthabsoevcetosrhoanwgslea ocfir3c8le.5o°f. rCaadlicuuslate: The diagram above shows a circle of radius
(a) the length of the minor arc
10.5cm with a sector angle of 60o.
18.3 cm with97a6 sectCorhaaptnerg18le ofT3rig8on.5om°e.trCy 2alculate: (a) th(eb)areaofththelmeningotrhseocftotrhemajorarc
T10h.e5dcimagwraimthabsoevcetosrhoanwgslea ocfir1c.l7e orafdriadnisu.s
(a) theareaofthe(ma)intohresaercetoaroftheminorsector (a) the area of the minor sector
10.5cmwithasec1to0r.5ancgmlewoifth1.a7sreacdtioarnas.ngleof1.7radians. 1C0a.l5cuclmatewtihthe arseeacotofrthaengmleinoofr1s.e7crtoadr.ians.
(b) the area of the major sector.
Calculate the area oCfatlhceulmatientohresaercetoaro. f the minor sector. Calculate the area of the minor sector.
(b) the area of the(mb)ajothreseacretoaro. f the major sector. (b) the area of the major sector.
88 12/11/2009
Fig. 18.22 Sector oFfiga. c1i8rc.2le2 Sector of a circle
Fig. 18.22 Sector of a circle
18.3 cm with a sec1to8r.3ancgmlewoifth38a.5se°.ctCoarlacnuglaleteo: f 38.5°. CaTlchueldatiea:gram aboveTshheodwisagaracmircalebovferasdhiouws s a circle of radius
Calculate the area of the minor sector.
976
976 976
Chapter18.indd Chapter 18
Chapter 18 Chapter 18
976
Trigonometry 2
T9ri7go6nometryC2hapter 18 Trigonometry 2 Trigonometry 2
10:43:09 AM
9.4 cm
9.4 cm
9.4 cm
9.4 cm
9.4 cm
80.o
80.78 80.78
80.78
80.78
80.78
9.4 cm
9.4 cm 9.4 cm
9.4 cm 9.4 cm
49.58 49.58
49.58
49.58
49.58
15.8 cm
15.8 cm
15.8 cm
15.8 cm 15.8 cm
10.51c0m.5cm 10.5 cm
10.5 cm
10.5 cm
1.7c 1.7c 1.7c
1.7c
1.7c
18.3 cm
18.3 cm
18.3 cm
18.3 cm 18.3 cm