,ytr tpepNahfj;jpw;fhf,ytr tpepNahfj;jpw;fhf,ytr tpepNahfj;jpw;fhf,ytr tpepNahfj;jpw;fhf,ytr tpepNahfj;jpw;fhf16

xU epiyj;j Gs;spapypUe;J khwhj; J}uj;jpy; mirAk; Gs;spxU epiyj;j Gs;spapypUe;J khwhj; J}uj;jpy; mirAk; Gs;spxU epiyj;j Gs;spapypUe;J khwhj; J}uj;jpy; mirAk; Gs;spxU epiyj;j Gs;spapypUe;J khwhj; J}uj;jpy; mirAk; Gs;spxU epiyj;j Gs;spapypUe;J khwhj; J}uj;jpy; mirAk; Gs;spxd;wpd; xOf;F tl;lkhFk;.xd;wpd; xOf;F tl;lkhFk;.xd;wpd; xOf;F tl;lkhFk;.xd;wpd; xOf;F tl;lkhFk;.xd;wpd; xOf;F tl;lkhFk;.

fPjh - ghj;jpkh> ,d;W mjpfkhd tisay;fs; mzpe;jpUf;fpd;wha;

mofhf cs;sJ.

ghj;jpkh - Mk;> vkJ khkh je;jhu;.

Nkhfdh - ghj;jpkh> tisaiyr; nra;a vLj;Js;s fk;gpapd; ePsk;

vt;tsT vd;gij mwpthah?

,g;ghlj;ijf; fw;gjd; %yk; ePq;fs;

tl;lj;jpd; gupjpiaAk; tpl;lj;ijAk; msf;fj;jf;f gy;NtWKiwfisg; gw;wpa tpsf;fk;

tl;;lj;jpd; gupjpf;Fk; tpl;lj;jpw;FkpilNa njhlu;GilikiacUthf;fy;

mj;njhlu;Gilikiag; gad;gLj;jp tl;lj;jpd; Miu> gupjpMfpatw;wpy; xd;W jug;gLk;NghJ kw;iwaijf; fzpj;jy;

jpdrupg; gzpfspy; ,j;njhlu;Gilikiag; gad;gLj;jy;vd;Dk; Nju;r;rpfis miltPu;fs;.

17xU tl;lj;jpd; gupjpxU tl;lj;jpd; gupjpxU tl;lj;jpd; gupjpxU tl;lj;jpd; gupjpxU tl;lj;jpd; gupjp

17.1 tl;lj;jpd; gupjpAk; tpl;lKk; 17.1 tl;lj;jpd; gupjpAk; tpl;lKk; 17.1 tl;lj;jpd; gupjpAk; tpl;lKk; 17.1 tl;lj;jpd; gupjpAk; tpl;lKk; 17.1 tl;lj;jpd; gupjpAk; tpl;lKk;

fhg;G &gh 1 ehzak ; &gh 2 ehzak; tz;br; rpy;Y

thfdr; rpy;Y Nahf;fl; %b ,Wtl;L fbfhu Kfk;

Njtp

Nahf;fl;

,ytr tpepNahfj;jpw;fhf,ytr tpepNahfj;jpw;fhf,ytr tpepNahfj;jpw;fhf,ytr tpepNahfj;jpw;fhf,ytr tpepNahfj;jpw;fhf 17

ghj;jpkh - vdf;Fj; njupahJ.

fPjh - tisay ; vd ; gJ tl ; l

tbtkhFk; . tisaiyr;

nra;ag; gad;gLj;jpa fk;gpapd;

ePsk; Rw;wsthFk;.

Nkhfdh - Mk;. ,q;F Rw;wsT gupjp

vdg;gLk;. fPjh mg;gupjpiaf;

fhZk; Kiwfis eP mwpthah?

fPjh - Mk;. tisaj;jpy; xU Gs;spiaf; Fwpj;Jf;nfhz;L xU

E}ypd; Edpia mt;tplj;jpy; itj;J kWgbAk; mg;Gs;sp

fpilf;Fk;tiu tisaiyr; Rw;wp E}iy itf;f. me;E}ypd;

ePsk; jhd; tisaypd; gupjp.

Nkhfdh - mt;tisaypy; xU

Gs;spiaf; Fwpj;J xU

NfhL topNa mjid

cUl;Lf. mg;Gs;sp

kWgbAk; Nfhl;bd; kPJ

tUk;NghJ tisay;

Nfhl;bd; kPJ xU Rw;Wr; Rw;wpapUf;Fk;. mf;Nfhl;bd; ePsk;

tisaypd; gupjpf;Fr; rkk;.

Nutjp - tisaypd; tp;l;lj;ijf; fhZk; Kiwia eP mwpthah?

fPjh - tpl;lk; vd;gJ ikaj;jpD}lhfr; nry;tJk; gupjp kPJ cs;s

,U Gs;spfisj; njhLg;gJkhd NfhlhFk;. ikaj;ijr;

rupahf mwpahtpl;lhy; tpl;lj;ij vg;gbf; fhzyhk;?

Nutjp - ftuhag;ngl;bapy; 2 %iykl;lq;fs; cs;sd. tiuNfhy;

kPJ tisaiy itj;J ,U %iykl;lq;fisAk; nrq;Nfhzk;

cs;s ,U gf;fq;fSk; tiuNfhiyAk; tisaiyAk;

mlf;fpapUf;FkhW itf;Fk;NghJ ,U cr;rpfSf;FkpilNa

cs;s J}uk; tl;lj;jpd; tpl;lkhFk;.

Nkhfdh- tl;lj;jpd; gupjpf ;Fk;

t pl ; lj ;j p w ;Fk pilNa

njhlu;G cs;sjh?

ehk; ,dp tl;lj;jpd;

gupjpf;Fk; tpl;lj;jpw;Fk;

,ilNa njhlu;G cs;sjh?

vdg; ghu;g;Nghk;.

,ytr tpepNahfj;jpw;fhf,ytr tpepNahfj;jpw;fhf,ytr tpepNahfj;jpw;fhf,ytr tpepNahfj;jpw;fhf,ytr tpepNahfj;jpw;fhf 19

,q;F π apd; ngWkhdk; 3'14 vdg; gad;gLj;jg;gLfpd;w NghjpYk; mjd;

ngWkhdk; 22

7 ,w;F mz;zsthfr; rkk; Mifahy; fzpg;Gfspy;

π =22

7 vdf; nfhs;sy; vspjhFk;.

xU tl;lj;jpd; Miu 10 cm MFk;. mjd; gupjpiaf; fhz;f.

^π = 3.14 vdf; nfhs;f.&

tl;lj;jpd; Miu (r) = 10 cm

tl;lj;jpd; gupjp (c) = 2πr

= 2 × 3.14 × 10 cm

= 62.8 cm

xU tl;lj;jpd; Miu 3.5 cm mjd; gupjpiaf; fhz;f.

^ =22

7 vdf; nfhs;f.&

tl;lj;jpd; Miu (r) = 3.5 cm

tl;lj;jpd; gupjp (c) = 2πr

= × ×2

22

73 5

2

1

. cm

= 22 cm

xU tl;lj;jpd; gupjp 44 cm vdpd; mjd; Miuiaf; fhz;f.

^ =22

7 vdf; nfhs;f.&

tl;lj;jpd; gupjp (c) = 44 cm

c = 2πr Mifahy;>

2πr = 44cm

222

7× × r = 44 cm

c = 2πr

cjhuzk; 17.1cjhuzk; 17.1cjhuzk; 17.1cjhuzk; 17.1cjhuzk; 17.1

cjhuzk; 17.2cjhuzk; 17.2cjhuzk; 17.2cjhuzk; 17.2cjhuzk; 17.2

cjhuzk; 17.3cjhuzk; 17.3cjhuzk; 17.3cjhuzk; 17.3cjhuzk; 17.3

,ytr tpepNahfj;jpw;fhf,ytr tpepNahfj;jpw;fhf,ytr tpepNahfj;jpw;fhf,ytr tpepNahfj;jpw;fhf,ytr tpepNahfj;jpw;fhf20

gapw;rp 17.1gapw;rp 17.1gapw;rp 17.1gapw;rp 17.1gapw;rp 17.1

44

7× r = 44 cm

44

7

7

44× × r =

7

4444× cm

r = 7cm

,U tl;lq;fspd; MiufSf;fp;ilNa cs;s tpfpjk; 2 : 3 MFk;.

mtw;wpd; gupjpfSf;fpilNa cs;s tpfpjj;ijf; fhz;f.

,U tl;lq;fspd; MiufSf;fpilNa cs;s tpfpjk; = 2 : 3

∴ Kjy; tl;lj;jpd; Miu 2x vdpd;> ,uz;lhk; tl;lj;jpd; Miu 3x MFk;.

mg;NghJ Kjy; tl;lj;jpd; gupjp = 2πr

= 222

7× × (2 )x

,uz;lhk; tl;lj;jpd; gupjp = 2πr

= 222

7× × (3 )x

gupjpfSf;fpilNa cs;s tpfpjk; = 222

72

22

7× × × ×(2 ) : (3 )x x

= 2 : 3

1. fPNo jug;gl;Ls;s mstPLfSf;Nfw;g xt;nthU tl;lj;jpdJk; gupjpiaf;

fzpf;f. ^π = 3.14 vdf; nfhs;f&.

(i) Miu 20 cm (ii) tpl;lk; 12 cm

(iii) Miu 9 cm (iv) tpl;lk; 15.2 m

2. gpd;tUk; mstPLfSf;Nfw;g xt;nthU tl;lj;jpdJk; gupjpiaf; fzpf;f.

^π =22

7

vdf; nfhs;f&.

(i) Miu 28 cm (ii) Miu 3.5 cm

(iii) tpl;lk; 10.5 cm (iv) tpl;lk; 19.6 cm

,U tl;lq;fspd; MiufSf;fpilNa cs;s tpfpjKk; mtw;wpd;gupjpfSf;fpilNa cs;s tpfpjKk; rkdhFk;.

cjhuzk; 17.4cjhuzk; 17.4cjhuzk; 17.4cjhuzk; 17.4cjhuzk; 17.4

,ytr tpepNahfj;jpw;fhf,ytr tpepNahfj;jpw;fhf,ytr tpepNahfj;jpw;fhf,ytr tpepNahfj;jpw;fhf,ytr tpepNahfj;jpw;fhf 21

3. gpd;tUk; gupjpfis cila tl;lq;fspd; Miufisf; fzpf;f.

(i) gupjp 66 cm (ii) gupjp 88 cm

(iii) gupjp 220 cm (iv) gupjp 330 m

4. xU Nkhl;lhu; thfdj;jpd; rpy;ypd; tpl;lk; 63 cm MFk;. thfdk; 2 km

J}uk; nry;ifapy; ,r;rpy;Y RoYk; KOr; Rw;Wfspd; vz;zpf;if ahJ?

5. xU fbfhuj;jpd; epkplf; fk;gp 4.2 cm ePsKs;sJ. gpd;tUk; Neuq;fspy;

mf;fk;gpapd; Kid nry;Yk; J}uk; jdpj;jdpahf vt;tsT?

(i) 60 epkplj;jpy;

(ii) 120 epkplj;jpy;

(iii) 30 epkplj;jpy;

(iv) 15 epkplj;jpy;

(v) 45 epkplj;jpy;

6. cUtpy; fhzg;gLk; miutl;l Nkilapd; tpl;lk; 7 m MFk;.

7.

cUtpy; Xu; Xl;lg; ghijapd; gUk;gbg; glk; cs;sJ. ,J xU

nrt;tfg; gFjpiaAk; ,U miutl;lg; gFjpfisAk; nfhz;Ls;sJ.

,r; nrt;tfg; gFjpapd; ePsk; 112 m ck; mfyk; 56 m ck; MFk;.

,g;ghijapd; Rw;wsitf; fhz;f.

56 m

112 m

,q;F tl;lg; gFjp topNa Xu; cNyhff; fPw;W nghUj;jg;gl;Ls;sJ.

mf;fPw;wpd; ePsj;ijf; fhz;f.

12

6

9 3

4.2 cm >>

>

> 7 m

,ytr tpepNahfj;jpw;fhf,ytr tpepNahfj;jpw;fhf,ytr tpepNahfj;jpw;fhf,ytr tpepNahfj;jpw;fhf,ytr tpepNahfj;jpw;fhf22

8. xU ad;dypy; nghUj;jg;gl;Ls;s Xu; ,Uk;G mspailg;gpd; (Grill)

fpilg;glk; cUtpy; fhzg;gLfpd;wJ. ,jw;Fg; gad;gLj;jg;gLk; fk;gpapd;

ePsj;ijf; fhz;f.

9. gpd;tUk; cUf;fspd; Rw;wsitf; fhz;f. vy;yh cUf;fspYk;

tpy;yhdJ miutl;lq;fshFk;.

10. cUtpy; xU ,ae;jpuj;jpd; nghwpg; gFjp fhzg;gLfpd;wJ. ,q;F

xd;Nwhnlhd;W njhLifAWk; NtWgl;l Miufs; cs;s ,U tl;lr;;

rpy;Yfs; cs;sd. xU rpy;Y RoYk;NghJ kw;iwa rpy;Yk;

RoYfpd;wJ. ,q;F ngupa rpy;Y xU Rw;Wr; RoYk;NghJ rpwpa

rpy;Y vj;jid Rw;Wr; RoYk;?

− −

−−

−

− −

−−

−

−−

−−

−

−−

− −

−−

−

14 cm 7 cm

1 4 c

14 cm

(i)

28 cm<

28 cm

>

><

(ii)

14 cm

14 cm

><

> <

− −−−

− −

−−

−

−−−−− −−−

,ytr tpepNahfj;jpw;fhf,ytr tpepNahfj;jpw;fhf,ytr tpepNahfj;jpw;fhf,ytr tpepNahfj;jpw;fhf,ytr tpepNahfj;jpw;fhf 23

11. ,q;F Xu; Xl;lg; ghijapd; fpilg;glk; fhzg;gLfpd;wJ. ,J xU

nrt;tfg; gFjpiaAk; ,U miutl;lg; gFjpfisAk; nfhz;Ls;sJ.

nrt;tfg; gFjpapd; ePsk; 112 m ck; tl;lg; gFjpapd; Miu 27.5 m

ck; MFk;. Xl;lg; ghij 1 m mfyKs;sjhf ,Uf;Fk; mNjNtis

xt;nthU jlitAk; Xl;lk; xOq;ifapd; eLtpy; eilngw Ntz;Lk;.

(i) Kjy; xOq;ifapy; XLgtu; flf;Fk; tl;lg;gFjpapd; Miu ahJ?

(ii) Kjy; xOq;ifapy; XLgtu; xU Rw;W XLifapy; nry;Yk; J}uj;ijf;

fhz;f.

(iii) Vohk;; xOq;ifapy; XLk; Nghl;bahsu; Nghl;bapd; njhlf;fj;jpNy

Kjy; xOq;ifapy; XLk; Nghl;bahsu; XLk; mNj J}uj;ij

XLtjw;F Kjy; xOq;ifapy; cs;s Nghl;bahsupYk; ghu;f;f

vt;tsT J}uk; Kd;dhy; Nghl;bia Muk;gpf;f Ntz;Lk;?

12. ,y;y tpisahl;Lg; Nghl;b xd;wpf;fhf 400m Xl;lg; ghijnahd;iw

mikf;f Ntz;bAs;sJ vdf; nfhs;f. ,t;Nthl;lg; ghijahdJ

fPNo cUtpy; fhl;lg;gl;Ls;sJ Nghd;W xU nrt;tfj;ijAk; ,uz;L

miutl;lq;fisAk; cs;slf;fp ,Uf;f Ntz;Lnkdpd; x ,w;Fk; y

,w;Fk; nghUj;jkhd %d;W njhFjp msTfisf; fhz;f.

x

y

rrr =