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25 000 cm3 = ….......dm3;

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1155ccmm

18cm 18cm 151
30cm
12cm 9cm 9cm 24cm
12cm 12cm
15cm
30cm 15cm

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10cm C10=cm10 cm h=h 10 cm 10cm 20cm
L= 3300ccmm
C= 10 cm = 20 cm
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b = 8cm h= 10 cm
r

r = 55ccmm

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49,4
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mu (cm) 5760
(cm) (cm)
17
2 2,5 16 14
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{ da[ dD ,u0t|kfc8j]t0hk’cmdwfh 1,5 cm c]t ,uoE|ad 65,10 g.
{ da[ 0D ,u0t|kfc8]j t0hk’cmdwfh 1,2 cm c]t ,uoE|ad 37,06 g.
{ da[ 7D ,u0t|kfc8]j t0hk’cmdwfh 2 cm c]t ,uoE|ad 83,52 g.
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km3 hm3 dam3 m3 dm3 cm3 mm3
1 1 5 000
00 0 7
2 002 342 000

0, 5 0 2

5 dm3 = 5000 cm3 ; 7 dam3 342 m3 = 7342 m3 ;
1 m3 = 1000 dm3 ; 2 hm3 2 dam3 = 2002 dam3;
1 km3 = 1000 hm3 ; 0,502 cm3 = 502 mm3 .

154

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cm,.........

#D ddta[4Da’|9qj’j;p-|vb’j dgxsaokI6[[m=]+dy,q,k[a9f5o0Ev#’F*c]2yf [A mgu[j ,aonjv49v5.doodE9a[kodAo4a’D oU]q’.lj
$]dttD f4 a[a’ov3Eud49|ctj;ldp6’|;h gm|b’j kjq -.;jbj’fgpLx|aoI’jb 6[gdxa[oalkId[6 dm;hkd+ ’,q 2,0cgu ml,oA pzkkj ;o3.09cmdkc’]t l6’ 9cm.
l’6 20 cmD groyj gvqkoE
12,5 cm

g,$nvj D .dla[.jol.Elj.8oj okE3o84k3o.s|0vhg;j ’8pd|a,a[b’jrD ,=fougEouD8Nv9kmkoujr9dNotgo,mAou[qjk=]1gy,0rk8yfojcmggmv,qkj ,qk.u7f|;Lk;j ,pl6’dq,5cm2; |;j pxjvo]q’.o34oEfaj’djk;D
|j;pdq,4mu|b’j ,u[=]y,kfgmqkj 35 cm3 |;j pdq,mulv’,u[=]y,kfgmqkj 25,2 cm3.

4k,;jkoEmuwj s^vvdoAo,u[=]y,kfgmqjk.fL c]t oEmujpa’gs^nvoaho,u[=]y,kfgmqkj

.fL

&D lt]vpoElt|bj’gxaoI6[da[lkdg-y’j ,u];’pk; 35 m, ];’d;hk’ 12 m c]t

g]yd 140 cm. 4hkgryoj xvj poE.lj.shpa’ 30 cm 9bj’9trP’0v[ltD 4k,;kj oEmuj

16j.oltfa’j dkj ; ,uma’\qf9ad]yfL

*D 86hxk|;j p|bj’,ugoNvmujrNo 1,5 cm2. 4hk4vdoE]q’wx.o86h 35 cm3; 4k,;kj ]t

fa[oE9tl6’gmqkj .fL

155

rkdmu !* dko;afcmdg;]k

[qf mu *& sq;|;j p;afcmdg;]k

I. dyf9tde

!D 9qj’8n,j 9eo;omujg\ktlq,.l[j jvo9Eg,afD
|bj’;ao,u DDDDDDDD -q;j 3,’S |bj’-qj;3,’,u DDDDDDD okmuS |bj’okmu,u DDDDDDD ;yokmuD
{ 9qj’la’gdfg[y’j ;ymu;k’9eo;o;afcmdg;]k.lgj lAo9eo;o]5j,oU c]h;0Po
9eo;omujg\ktlq,8n,j .lj9qo7q[m5d95f X2.00 j \kpg4y’ 2h 00mn; 2.50 j \kp
g4y’ 2h 50mn ).

02.00 j 2.50 j 8.40 j

2.25 j 3.15 j

{ 9q’j vtmy[kp;kj gxaospa’ 02.50 j + 0.25 j = 2.75 j 9b’j gxao 03.15 jສະຫງສ.ວວນ.ລິສຂະສິດ
@D ]qfgda’7ao|jb’vvd9kdlts;aootg0fg;]k 9h 30mn c]t .-hg;]kc]jo 2h

50mn 9b’j Ivfmjkc0dD 4k,;kj ]qf7aooAoIvfmkj c0dg;]k9ad3,’L
;ymucdhG

+ 9 h 30 mn 80 mn = …. h …. mn
2 h 50 mn 11h 80 mn = …. h …. mn

… h ... mn

.odko[;dsq;|j;pg;]kgIqk8hv’[;d DDDDDDDD da[ DDDDDDDDD c]t DDDDDDDD da[ DDDDDDDDD
4hkzqo[;d0v’ DDDDDDDDDD skds^kpd;kj *W 8hv’7yfgxao DDDDDDDDDD c]h;gvqk8nj,
.l[j jvo,u DDDDDDDD c]h;oAoD
#D mhk;7e wx8afzq, ]k;wxIvfIhko8afzq,g;]k 9h 15mn c]t vvd9kdIhko

g;]k 9h 50mn. 4k,;kj mhk;7ewfh16.j oIhko8afzq,fqoxko.fL

_ 9 h 50 mn ;ymucdhG
9 h 15 mn
grnvj 9t]q[9eo;o;afcmdg;]kgryjo]q[
… h .... mn okmu da[ DDDDDDDDDDDD c]t DDDDDDDDDDDD da[ DDDDDDDDDDDD

156

$D 7qoz6h|bj’0a[]qfvvd9kdfq’gsao g;]k 7h 45mn c]t wxIvfmkj c0d

g;]k 10h 25mmD 4k,;jk 7qoz6hoAo.-hg;]k0a[]qfwx8k,mk’fqoxko.fL

;ymucdhG

_ 10h 25mn 9h + 60mn +25mn _ 9h 85mn

7 h 45mn 7h 45mn

]q[[+wfh ....h ....mn

g,njv9eo;ookmu]q[dao[+wfh8hv’xPj o ! -q;j 3,’gxao DDDDDDDDD okmudvj o
9kdoAo9bj’gvqkwx8nj,.lj DDDDDDD D
&D 9q’j la’gdf8q;1jk’]5j,oU c]h;oe.-hcdh0=h8+wxD
8q;1jk’ !D * xu !#& ;ao
V# 8q;1kj ’ @D !@ -q;j 3,’ #& okmu

V)
!) xu $W& ;ao = !_ xu $W ;ao _* -qj;3,’ @)W okmu
phvo;jk ! xu ,u #*& ;ao
= $ ;ao $ -q;j 3,’ $ okmuD
ສະຫງສ.ວວນ.ລິສຂະສິດ
8q;1jk’ #D @# -q;j 3,’ ' & = 8q;1jk’ $D ( ;ao ' !@

@# -q;j 3,’ & ( ;ao !@

# $ -qj;3,’ #* okmu V @$ -qj;3,’ !$ -qj;3,’

V *W okmu !*) -q;j 3,’

!)W okmu W$)
W#W WW

W
dD ( ;ao ) -q;j w,’ V # CD @W -q;j 3,’ ' !&
0D !# -qj;3,’ &W okmu V _ 9D * okmu ' !@
7D $W okmu !& ;yokmu V ) lD & xu $ gfnvo ' )


II. .97;k,
!D sq;|j;p;afcmdg;]kc,jo;yokmuD laopt]adfh;p s ovd9kdoAopa’,uG
• okmu laopt]adfh;p mn

157

• -q;j 3,’ laopt]adfh;p h ສະຫງສ.ວວນ.ລິສຂະສິດ
g-yj’ 1mn = 60 s c]t 1h = 60 mn = 3600 s
@D dko[;dsq;|;j p;afcmdg;]kD

grnvj 9t[;d3,’F okmuF ;yokmuF gryoj [;d;yokmuda[;yokmuF okmuda[okmuF
3,’da[3,’D 4hkzqo[;d0v’;yokmuskdr=fu s^n s^kpd;kj *W gryjod=7yfw]jgxao
okmuc]h;gvqkwx[;d.loj kmuD 4hkzqo[;d0v’okmuskdr=fu s^n s^kpd;jk *W
gryjod=7yfw]gj xao-qj;3,’ c]h;gvqkwx[;d.lj-q;j 3,’D

#D dko]q[sq;|j;p;afcmdg;]kD
grnjv9t]q[sq;|;j p;afcmdg;]kF gryjo]q[;yokmuda[;yokmuS okmuda[okmu c]t
-q;j 3,’D da[-qj;3,’D g,njv;yokmu]q[dao[+wfh8hv’cpd ! okmu vvdgxao *W ;yokmu
c]h;gvqkwx8n,j .l;j yokmuD 4hkokmu]q[dao[+wfhd=8hv’cpd ! -q;j 3,’vvdgxao *W
okmu c]h;gvqkwx8nj,.loj kmuD

$D dko76osq;|j;p;afcmdg;]kD
dko76osq;|j;pg;]kgIqkgvqkc8]j tsq;|;j pg;]k X;yokmuF okmuF -qj;3,’F
;aoF gfnvoF xu? 76oda[8q;76o9kdoAo9bj’xPj o7noD

&D dkoskosq;|j;p;afcmdg;]kD
dkoskosq;|;j p;afcmdg;]kc,oj gIqkg]u,j sko9kdsq;|;j pmujs^kp]q’wxD
4hksq;|;j pmujs^kpsko[+wfhgIqk9txPj osq;|;j ps^kpoAo,kgxaosq;|j;pmuj
|hvp4af]q’,k c]h;skowx8k,]efa[D

III. [qfg/ydsaf

!D .ow]ptg;]k16j0hk’]5j,oUgmqkj da[9adokmu (mn) L

1h 25 mn; 3h 12 mn; 2h 32 mn

@D .ow]ptg;]k160j hk’]5,j oUgmqjkda[9ad;yokmu (s)?

3h; 2h 15 mn; 1h 8 mn; 3h 10 mn 25 s.

#D .ow]ptg;]k160j hk’]5,j oUgmqjkda[9ad-q;j 3,’ c]t 9adokmuL

144 mn; 78 mn; 235 mn; 138 mn.

158

$D .ow]ptg;]k160j hk’]5,j oUgmqkj da[9ad-qj;3,’S 9adokmu c]t 9ad;yokmuL

3820s; 4318s; 8155s; 7764s *D 9q’j gIafg]d]q[8+wxoU G
dD 17h 45mn – 12h 30mn
&D 9q’j [;d9eo;o8+wxoU 0D 11h 45mn – 8h 30mn
dD 2h 13mn + 1h 46mn
0D 7h45mn + 2h 51mn 7D 24mn 15s – 16mn 40s
7D 1h 43mn 30s + 3h 5mn 50s ’D 10h 35mn – 2h 50mn
’D 4h 38mn 40s + 2h 45mn 28s 9D 19h 14mn – 11h 28mn
9D 6h 54mn 25s + 11h 38mn 55s

(D 9qj’7yfw]gj ]d]5j,oUG ສະຫງສ.ວວນ.ລິສຂະສິດ
dD X@) ;ao !* -qj;3,’ T $ ;ao !) -q;j 3,’? V *
0D X!* -q;j 3,’ !W okmu _ # -qj;3,’ @W okmu? V $W
7D X!) -qj;w,’ & okmu $ ;yokmu T &* okmu? V @$
’D #W -q;j 3,’ ' @$
9D #W okmu ' !@ ;yokmu
lD ( -q;j 3,’ #W okmu ' @& okmu
-D # ;ao ' #* -qj;3,’
pD $ xu ( gfnvo ' !! gfnvo

)D dkolv[gla’;y-k7toyflkf,ug;]k 90mn c]t wfhg]uj,8Qog;]k 8h 30mmD
4k,;jkdkolv[gla’;y-k7toyflkfoAo 8hv’.shc]h;g;]k9ad3,’L

_D dkoc0’j 0aody]k[kolqj’wfhg]u,j 8Qog;]k 13h45mn c]t g]udg;]k 17h 16mnD
4k,;kj dkoc0’j 0ao[kolq’j oAo .-hg;]kgmqkj .fL

!WD c8jdvj o-kj ’spy[g7nvj ’z6h|b’j .-hg;]kspy[dtf6,|;j p]t & okmu ,kfP;oU
]k;.-hg;]kspy[dtf6,rP’c8|j j;p]t # okmuD 4k,;jk 4hk-k’z6hoAospy[
dtf6, #WW |;j p ]k;9txtspafg;]kwfhgmqkj .fL Xg,njvmP[.ljc8dj vj o?D

!!D ]qf0qolq’j 7ao|bj’c]jofh;p7;k,w; ! dy3]c,af 8+ @ okmu & ;yokmuD 4k,;kj
4hk]qf7aooAo c]oj fh;p7;k,w;f’aj dkj ;rkp.o !) okmu 9twxwfh9addy3]c,afL

159

[qf mu ** w]ptmk’F 7;k,w;F w]ptg;]k

I. dyf9tde

!D gInv[yo]e|b’j ,u7;k,w;ltg]pj $&Wkm / h, 4hk;kj gInv[yo]eoAo.-hg;]k[yo

& h; 2h 20 mn; 1h 12mn c]t 3h 15mn. c8]j tw]ptg;]k9twxwd9da d3y ]c,fa L

{ 9qj’la’gdfg[yj’;ymu7yfw]jw]ptmk’mujgInv[yowxwfh c]h;8nj,8k8t]k’]5j,oU

 rkp.o 5h gInv[yowxwfh $&Wkm / h V 5h = 2250 km

 rkp.o 2h 20mn gInv[yowxwfh

;ymu !G 450km # 140mn
60mn
450km/h # 2h20mn = 450km/h # 140mn = = 1050km

;ymu @G

450 # (2h20mn) = 450km/h # 2h + 450km/h # 20mn

= 900km + 450km # 20mn ສະຫງສ.ວວນ.ລິສຂະສິດ
60mn

= 900km + 150km = 1050km

w]ptg;]k 5h 2h 20mn 1h 12mn 3h 15mn
w]ptmk’ 2250km

@D 9qj’la’gdfg[y’j ;ymu7yfw]cj ]h;8nj,8k8t]k’]5,j oUD
8q;1jk’G dko-vdsk7;k,w;ltg]pj D

120km ' 4h = 30km/h

27km ' 1h30mn

27km ' 90 h = 27km # 60 h = 18km/h
60 90

w]ptg;]kmuwj xwfh 120km 325km 27km 189km
w]ptg;]k0v’dkowx 4h 5h 1h 30mn 2h 17mn
7;k,w;ltg]jp
30km/h

160

#D 9q’j la’gdfg[y’j ;ymu7yfw]jc]h;8n,j 8k8t]k’]5j,oUD

8q;1jk’G dko-vdskw]ptg;]kmu.j -h.odkog7nvj omujD

• 1700km ' 425km/h = 4h

• 536km ' 96km/h = 5h + 56 h
96

= 5h + 56 # 60mn = 5h + 35mn = 5h35mn
96

w]ptg;]kmuwj xwfh 1700km 536km 180km 840km
7;k,w;ltg]pj 425km/h 96km/h 75km/h 360km/h

w]ptg;]k0v’dkog7nvj omuj 4h

II. .97;k, ສະຫງສ.ວວນ.ລິສຂະສິດ

!D dko-vdskw]ptmk’D
gryoj -vdskw]ptmk’0v’dkog7njvomufj h;pdko76o7;k,w;ltg]jpda[w]
ptg;]k0v’dkog7nvj omuDj

w]ptmk’ = 7;k,w;ltg]pj V w]ptg;]k

4hkg;]k0v’dkog7nvj omusj kd[vdsq;|j;p8kj ’dao 8q;1kj ’G 3,’ c]t okmuD
gryoj 8hv’xjPo3,’gxaookmudjvo c]h;9b’j -vdskw]ptmk’ 3fp76o7;k,w;
da[g;]k0v’dkog7nvj omuDj
@D dko-vdsk7;k,w;ltg]pj D
gryoj -vdsk7;k,w;ltg]pj 0v’dkog7njvomuj fh;pdkoskow]ptmk’mujwfh
zjkowx.shg;]k0v’dkog7njvomujD

7;k,w;ltg]pj = w]ptmk’ ' w]ptg;]k

161

sq;|;j p0v’7;k,w;ltg]pj gxaody3]c,af8+-q;j 3,’ s^n gxaoc,af8+;yokmuS
4hkw]ptg;]kgxao3,’ c]t okmu8hv’xjPo3,’.shgxaookmugrnvj .shgxaosq;
|j;p1kj ’fP;daodvj o c]h;9b’j -vd7;k,w;8+|bj’okmu s^n 8+-q;j 3,’D

#D dko-vdw]ptg;]k0v’dkog7njvomuDj
gryoj -vdskw]ptg;]k0v’dkog7nvj omujfh;pdkoskow]ptmk’ Xmujzkj owx?
.sh7;k,w;ltg]jpD

w]ptg;]k = w]ptmk’ ' 7;k,w;ltg]pj

g,njv-vdsk9eo;o-jq;3,’wfhc]h; c]t 4hkpa’,uglf16jd=8hv’76ofh;p *W vud
c]h;9bj’sko8+wxgrnjv-vdskokmuF 4hkpa’,uglf16jvudd=8hv’76ofh;p *W vud
grnjv-vdsk;yokmuD

III. [qfg/ydsaf ສະຫງສ.ວວນ.ລິສຂະສິດ

!D ]qfgdJ’7ao|bj’c]oj fh;p7;k,w; 54km/h. 4hk]qf7aooAo.-hg;]kc]joG
4h; 2h 40mn; 1h 50mn; 35mn 9twxwfh9addy3]c,afL
@D mhk;]yovvd9kdgInvog;]k 9:45mn. grnjv9twx1k, mhk;cdh; ]k;7yf;kj

9twx.shIvfgInvomhk;cdh;g;]k 11:00 mn 8k,xqddt8yc]h;]k;pkj ’wfh
4km/hD 4k,;kj w]ptmk’c8jgInvo mhk;]yo skgInvo mhk;cdh; ,u9addy3]
c,af (km)L
#D 9qj’8nj,8k8t]k’]5,j oUD

w]ptg;]kmujwxwfh 81km 56km 11,76km 3555km
g;]kvvd9kd 7:50mn 14:35mn 12:33mn 11:45mn
g;]kwxg4y’ 10:05mn 15:17mn 15:00mn
w]ptg;]k0v’dkowx 5h 16mn
7;k,w;8+|b’j -q;j 3,’

162

ສະຫງສ.ວວນ.ລິສຂະສິດ$D mhk;[5o,u pjk’fh;p7;k,w; #F* km/h. grnjv9tpkj ’.shwfh $F@ km ]k;8hv’
.-hg;]k9ad-qj;3,’L

&D mhk;[5o,u c]t mhk;]yo -;odaowxmjP;l;o;afmtotme[aofkgzqjkmujmjk
okc]h’ g-yj’,uw]ptmk’ @W kmD mhk; [5o,u ;kj 9t0u]j qf9adwxfh;p7;k,w;
$) km/h c]t mhk;]yo ;kj 9t0uj]qf4u[wxfh;p7;k,w; !* km/h c8jg0qkma’
lv’7qowxIvfl;o;afmtotmerhv,dao.og;]k _GWW. 4k,;jkG

dD mhk;[5o,u .-hg;]kgfuomk’wxl;o;afmtotmegmqkj .fL
0D mhk;]yo .-hg;]kgfuomk’wxl;o;afmtotmegmqkj .fL
7D mhk;[5o,u vvd9kdgInvog;]k9ad3,’L
’D mhk;]yo vvd9kdgInvog;]k9ad3,’L

163

gr’-kf

-kf]k;8A’c8j.f,k ]k;m5dmq;j |hkg-uf-6l5f.9
I;j ,cI’I;j ,9yfIj;,.9 lk,ad7udaogxaode]a’fP;
gfaffPj ;rhv,daodhk;|hk [6-k-6dPf0v’]k;
lqj’glu,.-hlyfgxaog9Qk ]k;m5d-qogzqjkltg\urk[dao
[+.sh/6’9addtraf c]t r;d0kp-kfg0Qk,k]q[d;o
]k;ma’,;o-6gvdt]kf vyflts^trk[ 0v’-kf]k;w;h
8aflyo.9 l6h-u’gvqkw- rk-kfdhk;wxl6j7;k,;afmtokD

ສະຫງສ.ວວນ.ລິສຂະສິດ