MENSURATION

CHAPTER-1t L Aras Related to Cirles.)

CircleCirale 1she locas a boin uhuch moves

n such a uy hat tts ds kavre fom foved

Po1nt remauns ons tant

0 ixed ponk o called enle

Ex: Bangle. Coin heel , Moon, cUN, Unlouer

Papad

Crcunrense he boundaryperimeber ¢ a a'rale

Calleed its Circumeence

t s he dytanre Covened by tavellune oncCe anaund a ci'rde

Cirumsense.= 2Tr rddiw (onstant

3.14-E 22 q

Special Cast Ca R *Crrcumfenene o a crdle

2Y nd

y.Yadius ddaamees o the cirde

d-2 -2Y

Soln dráme tex of ceheel 84 cm adiuy qf. uheel 94 42 cm

lsance oened n I vevaluHon= 2 *22, 42

92 m 19200Cm =264cm

Ne o(onple eve.letry tp (over 292m -79200 264

= 300 '

ec:02 Avea of he Ctrcle[n2

Area d he Cirle = Area q the ectangle Jengthy breadlkn

Aveaot Helhele r

*Aea f he Semi Crcle= L*Y

Lengh of he Arck Ach

Axc lengh = Y9 Arc lengh 22r/8 36 otur hne:-

must be In adian

*Peuimeler a semicirle = Ar +2Y = Y(T+2 T+2) ccde Semi

2- * dustance moed y a uheel in lxotahm= CirCurmfenene

he wheel Nwmbon q RotaHon in 1minuet dútonce moved in Lnmërue

Ctrum enence Exam bles find he rumfnense o he uheel ycle Cehose dioumeter s 21 Cm SoLn dameter = 21 Cm

() aduj = 21 mf:dz 2r Y=d o S Cm

Urumenerse = 2 T = 2x2-14 x Jo:5= 66Cm An Ex-2 Ifhe diameBer o a semicirtde plot 1s 14m find its pouneler plot 1s 14m Phen Soln

d= I4m 2x =14 A

Perumeder = Semu (trtumfenenre t dsumeker ( AB) ACa) 22 +J4 3 6m An

Ex:-3 A wheelhas dionmeler 84 cm find oc ma Complek ealutions. must It niake fo (ovey 792 meler

Ex uhd wne o cirular pank uhoe uruunlnente tS 22m:

Soln et radius Crcle Ym Cimrence = 27Y = 22

= 22

H2 0At o Lircde z 38.5 m

EXTf he perimeter ard anea of a ciicle ane mumeutally equa hen find the radiiu he cirtle?

Son et raduuy Cde = Y

Hhen, perimefer od cirode = 2r

Aea arcle = TY Ach to uesthon

Avea g urde = pemejer f Citle

And

Ex difenence b/ ltufenente and diamefero Crtula at plot Is 105m ttnd dhe aea e the

Circulas þlot

Soln Crtemforence = 2NY

Da Drameter= *

Accn to question- 27Y-Y= 105

37( 32-)=ld = us F

=49

Area o Clrculas blot= TY 2(4

Ara of Circulos plot= 2449 =1886-5 m2

RThe vadif o tuo tircler ane 8cm Cnd 6Cm

espectiily e4utett. And ie radiiy o the Cide having t aiq equali to the Swm d he aneau the tue direles.

Cirde

Soln Area o1t icle = T62 36T

Avea of Secnd de =T $2= HT

Stum of oeaj o fd (ide =647 +36T

Aveg c new tirde = l0o

AR lo 0-

R= Jo Cm

Ex An umbrella has 8 hs which ane equally Spated Assumr sb wmbella be a flat tiicle

adiy 4Scm Aind anea b/w tuo Conictutie bs Fhe wnbeila .

Sol- Anea cHb = Lx Area o wmbrela

qdiy = re 45cm

x (4s) x yS XYS = * 205S

Arta f ib xanra ef unbretla x33 205s

28

Ana b/w tuo (onetuhive ih =***5cm Anu Ary

ARC: 03 Ara Related to the lrtle

ny teo

cherd A Jne Segnent Joining oy T

points on a ctrcde àcallecd a chord e he

Ctrtle

nhs qute ABs chord

A b-Studyonlune tlanes

chord

Secant- A June whuoh Tnterject a circde ara

tuo points on a cirtle called q cherd

he circle Secat

Tn thus ne EF s Se cant E F

Avc- Arc s peace o The ardle

wntter nhusHgwe AB S n ac and t S wntr

AB

AR

ongth ef he Arc Aß = e27 360

TY9 180

arENL2

Secor a Ctrtle

Hie yelm bourded by tuo radü d a chre

and e ane ntenpepted ey hem is calleol

Civcle sector Hhe

(E Poimeter of a Sector Ferumeter= 2T + 7

A

D Ara da sector:

Avea TY= TY'O°"| 360 360

r)Whn length He anc () Avn, Hhen

Area=Llr Snce= A9°

1g0

fb-Study onlune t las&ts

Example You Tube- Rankers Study oink

-1 A Sector i cut Yom a cirtle diameher

21Cm, I he anle g the secor i L50,

nd ts anea.

Soln Diameler 21¢m radiu = 2lcm

Ande of Jector =150*

Area of he sector= A= = 15y22/ 21 360 360

2 14f. 38 Cm

A sectoy 1s cut om a Circde orad1w tm

he angle sectox 120. tnd Hhe dengh o

Tts anc and aaiea

SCL eng o mc of sector angle 6 and radiis

120 22 H2 = 88 cm 180

Area he Sector = A= TYZ

360

2 120 22x(42) fb-Study onlune clawe

YeaTesbe Ranke study boirt 22 x6 Yy2

A = S?4S cm2

he lenghn gf m�nule hand o a clock s 14(m

end the ea Suept by the inutey hand

n 5 5 mrues.we TT=2

Sal enghh o muut) hand = 14 m

As, the minult havd 2otare un S munuks Area Cept by Hhe menuky hand = d

The Ene a of a sector agle 30°, tn a ctle

aadiuw 14Cm

The reuived omeq = G TY-3022y 14) cm The

360 360 J t cm2= S133 (m An

ec:04 Axa oa Segmert-

egment o a circle -

A Segmet qf a crtle is deJöned as he pant

C&le boundedby a choad and he. anc-

ADRO major

pont d cirtle

A AOBG IS

minor Segment

Cercle Rankers Study þeint / YouTube

major Segment and mrsr SEgment~

Hrea omuror seqmert=

Area ot Sector OAB- Area g tigle A

OAB

Abta of Sector OAB 1yRaue x height

x0A x OA XOB 360

y2 360

Rankes Study point/

You Tube Lr2sina

366

Shudy Onlune claAeL/ face book

Sins 2 360

aina Avea Munor segnment = /TS

360 2

Avea ma jor segment = Area c tie Circe - Ara af mùneY

eament

(360

3600

Ind ctle oYadiy a1cm an anc Jubtend age c6 t the Center

tird he lengh f ane Avea Hhe mroy Seqment 1 Avea he major segmen

SoLn. I LengHh o anc = Cm

360

331x 60 om 360

ATT B Cnm

Area mnor segmert=

Avea sector BA- anea of the A0AB OACR

=31 -sina m 31-Ix2Ixincoj|

231 H3 (m 4

45SER�2 40.05 cm

P Area o Hhe major Segment Area a the crtle - veag the me no Sernent

TY- 231) Cm2 = 93x21x al-231) Cm

1155 Cm

a Circle radiy 1SC

he Ex A chord A8

an angle 60' at Hhe Cenfes

ehe

egment, Subtends

Ctrole. And the ea mafay

and minor.

take 7r-3-14 , V3-113

Soln A= - she 366

one =ls cm. , and =66°

Hene

= (15)2 314x60 an 66", 360

22s3-m Cm 2

5 0.5233 -0-4325] (m

22Sx0.0 G08 cm

20.43 tm2

Area of major egment re o artle-Ared of munoY Sey_ met

= 3-14 x[Is)20-43? (m2

= 06 5 -20-43 cm2

2 686-04 cm Ans

Rarkers Stucly point /YouTube Sh- Study online clana

S find he anea he shaded designn side adjotnine t whoe AecD tS a squane e

IOcm and gemiciale ane dzawn. wth eacn Side he

Suane a diàmetey.

(R=3-14) B

C Soln D locm

b -16Cm

ocm- Avea regton Area o Reglon

ant ABCD

Meot ABGD - (sem AD +BC) SetmAB t CD

Jo0 SoT

00-2S 60-2S-26T =100 -S0T = Jo0-25S

Arta s haded egion= Aveaot ABCD -[Avea g I +I+I+1")

-25T- 5o -2)So(3-14-2) 54 An

00- 200-r)