xu tl;lj;jpd; gupjp - educational publications department g9 pii t... · 2014. 4. 12. · 20,ytr...
TRANSCRIPT
,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;?
− −
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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 =