This material is used for teacher and student of secondary level.

1. ul0ft z[ªvnf – % / ^
If]qldlt
P;Pn;L k/LIffsf] kl/dflh{t ljlzi6Ls/0f tflnsf 2065 cg';f/ If]qldltaf6 3 cf]6f 5f]6f] pQ/
cfpg] 6 cªs / 2 cf]6f nfdf] pQ/ cfpg] 8 cªs u/L hDdf 14 cªssf] 5 cf]6f k|Zgx¿ ;f]lwg]
k|fjwfg 5 . k/LIffnfO{ ;xof]uL x'g] s]xL dxŒjk"0f{ k|Zgx¿ pbfx/0f;lxt oxf“ k|:t't ul/Psf] 5 .
-s_ 5f]6f] pQ/ cfpg] k|Zgx¿
pbfx/0f M 1
ePsf] lqe'hsf] If]qkmn /
eP AB sf] gfk lgsfNg'xf]; .
;dfwfg M
xfdLnfO{ yfxf 5,
jf,
jf,
k]m/L, sf] If]qkmn (1)
jf,
jf,
jf, (1)
ctM AB sf] gfk = 8cm.
pbfx/0f M 2
k"/f ;txsf] If]qkmn ePsf] s'g} uf]nfsf] prfO lgsfNg' xf]; .
;dfwfg M lbOPsf], k"/f ;txsf] If]qkmn
uf]nfsf] prfO = ?
;"q cg';f/,
jf, (1)
jf,
jf,
ctM uf]nfsf] prfO / Jof; a/fa/ x'g] ePsf] n] prfO (1)
A
CB
10 cm

2. 2
pbfx/0f M 3
k"/f ;txsf] If]qkmn ePsf] juf{sf/ lk/fdL8sf] Pp6f e'hf
eP 58s] prfO lgsfNg'xf]; .
;dfwfg M oxf“, k"/f ;txsf] If]qkmn
juf{sf/ cfwf/sf] Pp6f e'hfsf] nDafO
58s] prfO
;'qfg';f/, k"/f ;txsf] If]qkmn ≠ cfwf/sf] If]qkmn lqe'hsf] ± 4 lqe'hsf] If]qkmn (1)
jf,
jf,
jf,
jf,
jf,
ctM 58s] prfO
pbfx/0f M 4
lbOPsf] lqe'hfsf/ lk|Hdsf] cfotg 5 . olb o;sf] prfO
/ cfwf/ ;de'h lqe'h 5 eg] lqe'hsf] Pp6f e'hfsf] nDafO
lgsfNg'xf]; .
;dfwfg M cfoftg
prfO
cfwf/sf] Pp6f e'hfsf] nDafO
;'q cg';f/, cfoftg cfwf/sf] If]qkmn prfO (1)
jf, (1)
jf,
jf,
jf, (1)
ctM cfwf/sf] Pp6f e'hfsf] nDafO /x]5 .
6
l
20 cm

3. pbfx/0f M 5
cfwf/sf] If]qkmnsf] b'O{ u'0ff jqm;txsf] If]qkmn ePsf] s'g} a]ngfsf] prfO
eP ;f] a]ngfsf] cw{Jof; lgsfNg'xf]; .
;dfwfg M a]ngfsf] prfO
a]ngfsf] cw{Jof;
k|Zg cg';f/, cfwf/sf] If]qkmn ≠ jqm;txsf] If]qkmn (1)
jf,
jf,
jf, (1)
ctM cw{Jof; /x]5 .
pbfx/0f M 6
;“u}sf] lrqdf lbOPsf] ;dsf]0fL lqe'hfsf/ cfwf/ ePsf] lk|Hdsf] k"/f ;txsf] If]qkmn lgsfNg'xf]; .
;dfwfg M
oxf“, lk|Hdsf] nDafO ℓ ;]=ld=
ABC sf] kl/ldlt (P) = 2.5+6.5+6
= 15 ;]=ld=
ABC sf] If]qkmn (A) =
= 7.5 ju{ ;]=ld= (1)
 lk|Hdsf] k"/f ;txsf] If]qkmn
= ℓ
=
= 15 + 375 = 390 ju{ ;]=ld= (1)
6.5 ;]=ld=
A A'
B B'
C C'25 ;]=ld=
2.5 ;]=ld=
6 ;]=ld
20 cm

4. 4
pbfx/0f M 7
lbOPsf] ;f]nLsf] (i) jqm;txsf] If]qkmn
(ii) k"/f ;txsf] If]qkmn
(iii) cfotg, kQf nufpg'xf]; .
{gf]6M 5f]6f] pQ/ cfpg] k|Zgdf Pp6f dfq cj:yf ;f]Wg] k|fjwfg 5 . }
;dfwfg M
lbOPsf] ;f]nLdf, OP =
= = = 48 ;]=ld= (1)
(i) jj|m;txsf] If]qkmn (CS) = rℓ ju{ ;]=ld== 2200 ju{ ;]=ld= (1)
(ii) k"/f ;txsf] If]qkmn (TS) = r r ℓ
= 44  64 = 2816 ju{ ;]=ld= (1)
(iii) cfotg (V) = r2h = 3=;]=ld= (1)
pbfx/0f M 8
Pp6f a]ngfsf] cw{Jof; 35 ;]=ld= / cw{Jof; / prfOsf] of]ukmn 65 ;]=ld= eP ;f] a]ngfsf]
jj|m;txsf] If]qkmn kQf nufpg'xf]; .
;dfwfg M
oxf“, j]ngfsf] prfO -h_= 65 – 35  r+h = 65 ;]=ld=  = 30 ;]=ld= (1)
jj|m;txsf] If]qkmn (CS) = 2rh
= 220  30 = 6600 ju{ ;]=ld= (1)
pbfx/0f M 9
Pp6f cw{uf]nfsf] k"/f ;txsf] If]qkmn 1039.5 ju{ ;]=ld= eP o;sf] cw{Jof; lgsfNg'xf]; .
;dfwfg M
oxf“, uf]nfsf] cw{Jof; (r) = ?
cw{uf]nfsf] k"/f ;txsf] If]qkmn (A) = 1039.5 ju{ ;]=ld=
A = af6 (1)
jf, ju{ ;]=ld=
jf,
;]=ld=
50 ;]=ld
P
O A

5.  r=10.5 ;]=ld= (1)
pbfx/0f : 10
Pp6f a]ngfsf/ 6of+sLdf 4200 ln6/ kfgL 5 . olb pQm 6of+sLsf] cw{Jof; 1.4m eP 6of+sLsf]
lk“w b]lv kfgL /x]sf] ;tx ;Ddsf] prfO{ lgsfNg'xf]; .
;dfwfg M
lbOPsf], 6of+sLsf] cfotg -kfgL /x]sf] dfq_
(V)= 4200 ln6/
=42001000 cm3 [ ln6/ ]
6of+sLsf] cw{Jof; (r) = 1.4m = 140cm
6of+sLdf /x]sf] kfgLsf] prfO{ (h) = ?
;'qcg';f/, V = r2h (1)
or,
or,
or, h = 68.14cm (1)
 pQm 6of+sLdf lk“wb]lv kfgL /x]sf] ;tx;Ddsf] prfO{ 68.14 ;]=dL= /x]5 .
pbfx/0f M 11
1m nfdf] Ps 6'qmf kmnfdsf] kfOksf] aflx/L cw{Jof; 10cm / leqL cw{Jof; 9cm eP hDdf
kmnfdsf] cfotg lgsfNg'xf]; .
;dfwfg M
lbOPsf], kfOksf] prfO{ (h) = 1m = 100 cm
aflx/L cw{Jof; (r1) = 10cm
leqL cw{Jof; (r2) = 9cm
kmnfdsf] cfotg (V) = ?
;'qcg';f/,
(1)
(1)
9 cm
10 cm

6. 6
pbfx/0f : 12
prfO{ 12 cm / Pp6f e'hf 8cm ePsf] ;dafx' lqe'hfsf/
cfwf/ ePsf] lk/fld8sf] cfotg lgsfNg'xf]; .
;dfwfg M
oxf“, lbOPsf lk/fld8sf] prfO{ (h) = 12cm
lqe'hfsf/ cfwf/ ePsf] ;dafx' lqe'hsf] Pp6f e'hfsf] nDafO{ (a) = 8cm
lk/fld8sf] cfotg (V) = ?
;'qcg';f/, cfwf/sf] If]qkmn (A) = -hxf“ _
=
= 27.71cm2 (1)
km]/L, cfotg (V) = cfwf/sf] If]qkmn  prfO{ =
=
 V = 110.84 c (1)
pbfx/0f : 13
cfwf/sf] cw{Jof; 14cm ePsf] ;f]nLsf] k"/f ;txsf] If]qkmn
1496 cm2
eP 58s] prfO{ kQf nufpg'xf]; .
;dfwfg M
lbOPsf], cfwf/sf] cw{Jof; (r) = 14cm
k"/f ;txsf] If]qkmn (A) = 880cm2
, 58s] prfO{ (ℓ ) = ?
;'qcg';f/,
k"/f ;txsf] If]qkmn = cfwf/sf] If]qkmn ± aqm ;txsf] If]qkmn
or, A = r2 + rℓ (1)
or, 1496 =
or, 1496 – 616 = 44ℓ
or, 880 = 44ℓ
ℓ=?
r=14 cm
8 cm
12 cm

7. or, = ℓ
 ℓ = 20cm (1)
dfly lbOPsf pbfx/0fx¿sf] ;xfotfn] lgDg ;d:ofx¿ ;dfwfg ug'{xf]; M
1. / ePsf] ;dlåe'h sf] If]qkmn
eP AB sf] gfk lgsfNg'xf]; . -pQ/ M _
2. / If]qkmn ePsf] sf]
sf] sf] gfk lgsfNg'xf]; . -pQ/ M _
3. k"/f ;txsf] If]qkmn 9856 cm2
ePsf] uf]nfsf] prfO lgsfNg'xf]; . -pQ/ M _
4. 38.808 cm3
cfotg ePsf] uf]nfsf] prfO lgsfNg'xf]; . -pQ/ M _
5. k"/f ;txsf] If]qkmn 451 cm2
ePsf] juf{sf/ kL/fld8sf] Pp6f e'hf eP 58s]
prfO lgsfNg'xf]; . -pQ/ M _
6. k"/f ;txsf] If]qkmn 400 cm2
ePsf] juf{sf/ kL/fld8sf] 58s] ;tx eP cfwf/sf]
Pp6f e'hfsf] nDafO lgsfNg'xf]; . -pQ/ M _
7. lbOPsf lqe'hfsf/ lk|Hdsf] cfotg 5 . olb o;sf]
prfO / cfwf/ ;de'h lqe'h 5 eg] lqe'hsf] Pp6f e'hfsf]
nDafO lgsfNg'xf]; . -pQ/ M _
8. Pp6f lqe'hfsf/ lk|Hdsf] cfotg 5 . olb o;sf] cfwf/ ;de'h lqe'h 5
h;sf] nDafO eP lk|Hdsf] prfO{ lgsfNg'xf]; . -pQ/ M _
9. cfwf/sf] If]qkmnsf] tLgu'0ff aqm ;txsf] If]qkmn ePsf] Pp6f j]ngfsf] prfO 12 cm eP
;f] j]ngfsf] cw{Jof; lgsfNg'xf]; . -pQ/ M 8cm_
10. cfwf/sf] If]qkmnsf] rf/u'0ff aqm ;txsf] If]qkmn ePsf] Pp6f j]ngfsf] prfO 24 cm eP
cw{Jof; lgsfNg'xf]; . -pQ/ M 12cm_
A
B C
1200
12 cm
P
Q R
12 cm
25 cm

8. 8
21 ;]=ld=
11. lbOPsf lqe'hfsf/ lk|Hdx¿sf] k"/f ;txsf] If]qkmn / cfotg lgsfNg'xf]; .
(a) (b)
-pQ/ M 288 ju{ ;]=ld= / 240 3=;]=ld=_ -pQ/ M 126 ju{ ;]=ld=, 162 3=;]=ld=_
(c)
-pQ/ M 144 j=;]=ld=, 300 3=;]=ld=_
gf]6 M 5f]6f] pQ/ cfpg] k|Zgdf If]qkmn jf cfotg s'g} Pp6f dfq ;f]lwg]5 .
12. lbOPsf] cw{uf]nf / ;f]nLsf] jj|m ;tx, k"/f ;txsf] If]qkmn / cfotg lgsfNg'xf]; .
(i) (ii)
pQ/ M77 ju{ ;]=ld=,115.5 ju{ ;]=ld=,89.83 3=;]=ld=
-pQ/M550j=;]=ld=,704j=;]=ld=,12323=;]=ld=_
gf]6 M 5f]6f] pQ/ cfpg] k|Zgdf If]qkmn / cfotg dWo] s'g} Psdfq ;f]lwg]5 .
13. lbOPsf] lk|Hdsf] 58s] ;txsf] If]qkmn lgsfNg'xf]; . -pQ/ M 360 ju{ PsfO _
14. ;de'hfsf/ lqe'hsf] If]qkmn eP AB sf] gfk kQf nufpg'xf]; .
-pQ/ M 6 cm_
15. Pp6f uf]nfsf/ j:t'sf] cfotg eP To;sf] Jof; slt xf]nf < -pQ/ M 1cm_
A A'
B B'10 ;]=ld=
P P'
Q'
P P'
Q Q'
R R'
8 ;]=ld=
7 ;]=ld=
9 ;]=ld=
;]=ld=
C C'
6 ;]=ld=
10 ;]=ld=
10 ;]=ld=
=25 ;]=ld=
O A
h =24 ;]=ld
P
Q
R R'
6 ;]=ld= ;]=ld=
A
B C
8 ;]=ld=
6 ;]=ld= 15 ;]=ld=

9. 16. lbOPsf] lk|Hdsf] cfotg 450 cm3
eP prfO{ kQf nufpg'xf]; .
-pQ/ M 15 cm_
17. Pp6f ;f]nLsf] jqm ;txsf] If]qkmn 440cm2
/ 58s] prfO{ 14cm eP cw{Jof; slt xf]nf <
-pQ/ M 10cm)
18. jqm ;txsf] If]qkmn 210cm2
ePsf] s'g} a]ngfsf] prfO{ 10cm eP cw{Jof; kQf
nufpg'xf]; . -pQ/M 10.5cm _
19. s'g} uf]nfsf] aqm ;txsf] If]qkmn 16cm2
eP uf]nfsf] cw{Jof; slt xf]nf < -pQ/ M 2cm_
20. k"/f ;txsf] If]qkmn 418cm2
ePsf] ;f]nLsf] cw{Jof; 7cm / cw{Jof; / prfOsf] of]ukmn
19cm eP 58s] prfO kQf nufpg'xf]; . -pQ/ M 12cm_
21. Pp6f ;f]nLsf] cfotg 13860cm3
/ prfO{ 30cm 5 . o;sf] cw{Jof; slt xf]nf <
-pQ/ M 21cm_
22. s'g} a]ngfsf] cw{Jof; / prfO{sf] of]ukmn 17cm / cfwf/sf] kl/lw 44cm eP k"/f ;txsf]
If]qkmn kQf nufpg'xf]; . -pQ/ M 748cm2
_
23. Pp6f ;f]nLsf] 58s] ;txsf] prfO{ 10cm / prfO{ 8cm eP aqm ;txsf] If]qkmn
lgsfNg'xf]; .
-pQ/ M 188.75 cm2
_
24. prfO{ 12cm / Pp6f e'hf 10cm ePsf] ;dafx' lqe'hfsf/ cfwf/ ePsf] lk/fld8sf] cfotg
lgsfNg'xf]; . -pQ/ M _
25. Pp6f e'hf 12cm ePsf] ;dafx' lqe'h cfwf/ ePsf] Pp6f lgoldt 6]6«fx]8«g (Regular
tetrahodron) sf] k"/f ;txsf] If]qkmn lgsfNg'xf]; . -pQ/ M _
26. hldg d'lg /x]sf] Pp6f a]ngfsf/ 6of+sLsf] Ifdtf 41580 ln6/ 5 . olb pQm 6of+sLsf]
cw{Jof; 2.1cm eP prfO{ kQf nufpg'xf]; . -pQ/ M 3 m_
27. aflx/L cw{Jof; 7cm / leqL cw{Jof; 6.9 cm ePsf]
14cm nfdf] kfOkdf ePsf] 7f]; j:t'sf] cfotg
lgsfNg'xf]; . -pQ/ M 61.16cm3
_
28. cfwf/sf] cw{Jof; 21cm ePsf] ;f]nLsf] k"/f ;txsf] If]qkmn 3366cm2
eP 58s] prfO{
lgsfNg'xf]; . -pQ/ M 30cm_
8 cm
10 cm
10 ;]=ld=
6 ;]=ld=

10. 10
29. cfwf/sf] If]qkmn 1386 cm2
/ prfO{ 50 cm ePsf] ;f]nLsf] cfotg lgsfNg'xf]; .
-pQ/ M 69300 cm3
_
30. prfO{ / cw{Jof; a/fa/ ePsf] j]ngfsf] cfotg 68992cm3
5 eg] prfO{ slt xf]nf <
-pQ/M28 cm_
-v_ nfdf] pQ/ cfpg] k|Zgx¿ M
pbfx/0f M 1
;“u} lbOPsf] lrq ;f]nL / a]ngfåf/f ag]sf] ;+o'Qm 7f]; j:t'sf] xf] . ;f]sf] k"/f ;txsf] If]qkmn /
cfotg lgsfNg'xf]; .
;dfwfg M
lbOPsf] lrqcg';f/,
OP = 54 – 30 = 24 ;]=ld=
OA = ;]=ld== 7 ;]=ld=
AP =
= = 25 ;]=ld= (1)
ca, k"/f ;txsf] If]qkmn (TS) = r2
+ 2rh + rℓ
= r(r+2h+ℓ) (1)
=
= 22  92 ju{ ;]=ld== 2,024 ju{ ;]=ld= (1)
cfotg (V) = r2
h + r2
h1 (1)
= r2
=
= 154  38= 5,852 3=;]=ld= (1)
pbfx/0f M 2
;“u}sf] lrq Pp6f ;f]nL / Pp6f cw{uf]nf ldn]/ ag]sf] ;+o'Qm 7f]; xf] . ;f] 7f];sf] k"/f ;txsf]
If]qkmn lgsfNg'xf]; .
;dfwfg M
oxf“, Aof; , cw{Jof;
;+o'Qm 7f];sf] prfO = 31 ;]=ld=
;f]nL cfsf/ efusf] prfO (h) = 31–7=24 ;]=ld=
30 ;]=ld=
54 ;]=ld=
14 ;]=ld=
P
A
O
O
B
A
31 ;]=ld=
14 ;]=ld=

11. 58s] prfO AB ℓ
AB = =
= =
 AB(ℓ) = 25 ;]=ld= (1)
tNnf] efu ;f]nLsf] aqm ;txsf] If]qkmn
ℓ
= 550 ju{ ;]=ld= (1)
dflyNnf] efu cw{uf]nfsf] aqm;txsf] If]qkmn
= 308 ju{ ;]=ld= (1)
t;y{, ;+o'Qm 7f];sf] k"/f ;txsf] If]qkmn = = 550 + 308
= 858 ju{ ;]=ld= (1)
pbfx/0f M 3
;“u} lbOPsf] lrq cfwf/ ju{ ePsf] lk/fld8sf] xf] . ;f]sf] k"/f ;txsf] If]qkmn / cfotg
lgsfNg'xf]; .
;dfwfg M
OM = BC = ;]=ld== 5 ;]=ld= (1)
OP = = = = 12 ;]=ld= (1)
k"/f ;txsf] If]qkmn TS ℓ2 + 4
= (BC)2
+ 4( CDPM)
= (10 ;]=ld=)2
+ 2  10  13 ju{ ;]=ld=
= 100 ju{ ;]=ld=+ 260 ju{ ;]=ld== 360 ju{ ;]=ld= (1)
cfotg (V) = ℓ2h =  10  10  12 3=;]=ld== 400 3=;]=ld= (1)
pbfx/0f M 4
Pp6f juf{sf/ cfwf/ ePsf] lk/fld8sf] cfotg
3
4000
cm3
/ cfwf/ e'hfsf] cfwf prfO{ eP
lqe'hfsf/ ;txx¿sf] If]qkmn lgsfNg' xf]; .
;dfwfg M
M
DA
13 ;]=ld=
CB
10 ;]=ld=
O
P
O

12. 12
lbOPsf] cfotg (V)=
3
4000
cm3
58s] ;txsf] If]qkmn (A) = ?
juf{sf/ cfwf/sf] e'hfsf] nDjfO = a cm dfgf} .
ctM lk/fld8sf] prfO{ (h) =
2
a
cm
;'q cg';f/, (V) =
2
..
3
1 2 a
a (1)
or,
2
.
3
1
3
4000 3
a

or, 3
8000 a
cma 20 (1)
km]/L, 58s] prfO kQf nufpg,
ON2
= OM2
+ MN2
=
=
= 200 (1)
 ON = 14.14cm
ctM 58s] ;txsf] If]qkmn (A) =
= 565.6 cm2
(1)
pbfx/0f : 5
Pp6f ;f]nLsf] k"/f ;txsf] If]qkmn 27456cm2
/ aqm ;txsf] If]qkmn 17600cm2
eP prfO{ kQf
nufpg'xf]; .
;dfwfg,
lbOPsf], ;f]nLsf] k"/f ;txsf] If]qkmn = 27456 cm2
= 17600 cm2
prfO{ = ?
ca, cfwf/sf] If]qkmn -j[Qsf] If]qkmn_ = k"/f ;txsf] If]qkmn — aqm ;txsf] If]qkmn
= 27456 – 17600
= 9856 cm2
(1)
a
O NMM
10 cm
? cm
A
BO

13. cw{Jof; kQf nufp“bf, A = r2
or,
or,
or,
 r=56 cm (1)
km]/L, 58s] prfO{ ℓ kQf nufp“bf,
A = rℓ
or, 17600 =
or,
 ℓ = 100 cm (1)
;f]nLsf] prfO kQf nufp“bf,
=
82.84 cm (1)
pbfx/0f : 6
Pp6f a]ngfsf] cw{Jof; / prfO{sf] cg'kft 3:4 5 . olb a]ngfsf] cfotg 310464 cm3 eP
cw{Jof; slt xf]nf <
;dfwfg M
lbOPsf], –––––––––– = cyjf cw{Jof; (r) = prfO{ (h) (1)
cfotg (V) = 310464
;'qcg';f/, V = r2h (1)
or, 310464 =
or, 175616 = h3
or, h = 56cm (1)
km]/L, cw{Jof; kQf nufp“bf,
r =
=
cw{Jof; (r)
prfO{ (h)

14. 14
= 42cm (1)
pbfx/0f M 7
;“u} lbOPsf] lrq cfwf/ ju{ ePsf] lk/fld8sf] xf] . h;sf]
58s] ;txsf] Pp6f lsgf/f 10 ;]=ld=/ 58s] prfO 8 ;]=ld=
eP lk/fld8sf] k"/f ;txsf] If]qkmn lgsfNg'xf]; .
;dfwfg M
lbPsf], lk/fld8sf] 58s] prfO AB = 8 ;]=ld=
Pp6f lsgf/f AC = 10 ;]=ld=
-gf]6M ;a} wf/x¿ a/fj/ x'G5g ._
k"/f ;txsf] If]qkmn = ?
xfdLnfO{ yfxf 5, kfOyfuf]/; ;fWo cg';f/
jf
jf
jf
jf
 BC = 6 cm (1)
t;y{, cfwf/ e'hf DC = ;]=ld= (1)
k"/f ;txsf] If]qkmn = 4 lqe'hx¿sf] If]qkmn + cfwf/sf] If]qkmn (1)
=4   DC  AB + DC2
=4   12  8 + 122
=192 + 144
=336 cm3 (1)
ctM k"/f ;txsf] If]qkmn =336 j=;]=ld= .
pbfx/0f M 8
jqm ;txsf] If]qkmn 3960 cm2
/ cfotg 41580 cm3
ePsf] s'g] j]ngfsf]
prfO kQf nufpg'xf]; .
8 ;]=ld=
10 ;]=ld=
D
A
CB
A
B
C
8 ;]=ld= 10 ;]=ld=

15. ;dfwfg M lbOPsf], jqm ;txsf] If]qkmn (A) = 3960 cm2
cfotg (V) = 41580 cm3
prfO (h) = ?
ca, A = 2rh
jf,
jf,
jf, ………… (i) (1)
k]m/L, (1)
jf,
jf, [ ;= (i) af6]
jf,
jf, (1)
ctM cw{Jof; ;]=ld=,
To;}n], ;= (i) af6,
jf, ;]=ld=, (1)
ctM prfO ;]=ld=,
pbfx/0f M 9
jqm ;txsf] If]qkmn 27.72 cm2
ePsf] cw{uf]nfsf] k"/f ;txsf] If]qkmn
/ cfotg lgsfNg'xf]; .
;dfwfg M jqm ;txsf] If]qkmn (A) =27.72 cm2
k"/f ;txsf] If]qkmn (TSA) = ?
cfotg (V) = ?
ca, (1)
jf,
jf,
jf,

16. 16
jf, (1)
t;y{, cw{Jof;
k]m/L, TSA (1)
cfotg kQf nufp“bf,
(1)
pbfx/0f M 10
tLgcf]6f 7f]; uf]nfx¿nfO{ kufn]/ Pp6f 18 cm cw{Jof; ePsf] 7f]; uf]nf agfOPsf] 5 . olb
b'O{cf]6f uf]nfx¿sf] cw{Jof; 2 cm / 12 cm eP t];|f] uf]nfsf] cw{Jof; lgsfNg'xf]; .
;dfwfg M
klxnf] uf]nfsf] cfotg (r1) =2 cm, bf];|f] uf]nfsf] cw{Jof; (r2) =12 cm / t];|f] uf]nfsf]
cw{Jof; (r3) = ?
klxnf] uf]nfsf] cfotg
bf];|f] uf]nfsf] cfotg
tLgcf]6f uf]nf kufn]/ agfOPsf] 7f]; uf]nfsf] cfotg
k|Zg cg';f/,
jf,
jf,
jf,
jf,
jf,

17. ctM t];|f] uf]nfsf] cw{Jof;
dfly lbOPsf pbfx/0fx¿sf] ;xfotf lnO{ lgDglnlvt ;d:ofx¿ ;dfwfg ug'{xf]; M
1. lbOPsf ;+o'Qm 7f]; j:t'x¿sf] k"/f ;txsf] If]qkmn / cfotg lgsfNg'xf]; .
(i) (ii)
pQ/ M 5,600.57 j=;]=ld=, 14,117.01 3=;]=ld= pQ/ M 506 ju{ ;]=ld=, 731.5 3=;]=ld=
(iii) (iv)
pQ/ M 858 ju{ ;]=ld=1,950.67 3=;]=ld= pQ/ M 792 ju{ ;]=ld=1,848 3=;]=ld=
2. ;“u} lbOPsf] lrq cfwf/ ju{ ePsf] lk/fld8sf] xf] .
olb o;sf] k"/f ;txsf] If]qkmn 552 ju{ ;]=ld= /
cfwf/sf] ju{sf] nDafO 12 ;]=ld= eP ;f] lk/fld8sf]
58s] prfO kQf nufpg'xf]; . ;fy} o;sf] cfotg
;d]t lgsfNg'xf]; .
pQ/ M 25 ;]=ld= 1568 3=;]=ld=
3. ;“u}sf] lrqdf lbOPsf] 7f]; j:t' juf{sf/ cfwf/ ePsf]
lk/fld8 xf] . olb PQ=24 ;]=ld= / PC=26 ;]=ld= eP
;f] lk/fld8sf] cfotg lgsfNg'xf]; .
pQ/ M 2908 3=;]=ld=
4. Pp6f juf{sf/ cfwf/ ePsf] lk/fld8sf] cfwf/ e'hfsf] nDafO{ 10cm / k"/f ;txsf] If]qkmn
420cm2
eP prfO{ kQf nufpg'xf]; . -pQ/ M 15.19cm_
5. Pp6f juf{sf/ cfwf/ ePsf] lk/fld8sf] cfotg 4500cm3
/ cfwf/ e'hfsf] cfwf prfO{ eP
o;sf] lqe'hfsf/ ;txx¿sf] If]qkmn lgsfNg'xf]; . -pQ/ M 1272.6cm2
_
6. Pp6f e'hf 24 cm nfdf] ePsf] juf{sf/ cfwf/ ePsf] lk/fld8sf] k"/f ;tsf] If]qkmn
1200cm2
eP lk/fld8sf] 58s] prfO{ kQf nufpg'xf]; . -pQ/ M 13cm_
14 ;]=ld=
A
P
27 ;]=ld=
12.5 ;]=ld=
15 ;]=ld=
36 ;]=ld=
25 ;]=ld=
P P'O
x 2x
A
P
M
D
O
A
C
B
14 ;]=ld=
37 ;]=ld=
15 ;]=ld=
24 ;]=ld=
Q
D
C
A
P
B
26 ;]=ld=
24 ;]=ld=

18. 18
7. 210cm nfdf] Pp6f kmnfdsf] kfOksf] leqL cw{Jof; 19cm / cfotg 25740cm3
eP
aflx/L cw{Jof; kQf nufpg'xf]; . -pQ/ M 20cm_
8. jqm ;txsf] If]qkmn 12.32cm2
ePsf] Pp6f cw{uf]nfsf] k"/f ;txsf] If]qkmn / cfotg
lgsfNg'xf]; . -pQ/ M 18.485cm2
/ 5.74cm3
_
9. 1cm, 6cm / 8cm cw{Jof; ePsf] tLgcf]6f 7f]; uf]nfx¿nfO{ kufn]/ Pp6f cw{uf]nf
agfOPsf] 5 . pQm cw{uf]nfsf] cw{Jof; slt xf]nf < -pQ/ M 18cm_
10. Pp6f ;f]nLsf] k"/f ;txsf] If]qkmn 6864cm2
/ jqm ;txsf] If]qkmn 4400cm2
eP ;f]nLsf]
prfO{ kQf nufpg'xf]; . -pQ/ M 41.42cm_
11. s'g} ;f]nLsf] k"/f ;txsf] If]qkmn 3036cm2
/ jqm ;txsf] If]qkmn 1650cm2
eP cfwf/sf]
cw{Jof; lgsfNg'xf]; . -pQ/ M 21cm_
12. cfwf/sf] cw{Jof; 7cm / 58s] prfO{ 15cm ePsf] ;f]nLsf] cfotg slt xf]nf <
-pQ/ M 680.68cm2
_
13. Pp6f a]ngfsf] cfwf/sf] cw{Jof; / prfOsf] cg'kft 4:5 5 . olb a]ngfsf] cfotg
eP cw{Jof; kQf nufpg'xf]; . -pQ/ M 60cm_
14. s'g} a]ngfsf] cfwf/sf] cw{Jof; / prfOsf] cg'kft 3:5 5 . olb a]ngfsf] aqm ;txsf]
If]qkmn eP cfotg kQf nufpg'xf]; . -pQ/ M 3818.57cm2
_
15. lbOPsf] sf7sf] a]ngfsf/ k]lG;nsf] sf7sf] Ps efudf
cw{uf]nfsf/ O/]h/ c8ofOPsf] 5 . olb k]lG;nsf]
sf7sf] nDafO{ 28cm / Jof; 1.4cm 5 eg] k"/f
k]lG;nsf] cfotg lgsfNg'xf]; . -pQ/ M 43.83cm3
_
16. Pp6f ;f]nLsf] cw{Jof; 14cm / k"/f ;txsf] If]qkmn 1848cm2
eP prfO{ slt xf]nf <
-pQ/ M 24.24cm_
17. 58s] ;txsf] Pp6f wf/ 13cm / 58s] prfO 12cm ePsf]
juf{sf/ kL/fld8sf] k"/f ;txsf] If]qkmn lgsfNg'xf]; .
-pQ/ M 260 cm2
_
18. 58s] prfO 4cm ePsf] juf{sf/ lk/fdL8sf] k"/f ;txsf] If]qkmn 84cm2
eP cfwf/sf]
Pp6f e'hfsf] nDafO lgsfNg'xf]; .
-pQ/ M 6 cm_
19. jqm ;txsf] If]qkmn 3080 cm2
/ cfotg 21560 cm3
ePsf] s'g} j]ngfsf] prfO kQf
nufpg'xf]; . -pQ/ M 35cm_
28 ;]=ld=
1.4 ;]=ld=
12 ;]=ld=
13 ;]=ld=

19. 20. cfotg 11000 cm3
/ jqm ;txsf] If]qkmn 2200 cm2
ePsf] j]ngfsf] prfO kQf
nufpg'xf]; . -pQ/ M 35cm_
21. jqm ;txsf] If]qkmn 1232 cm2
ePsf] cw{uf]nfsf] k"/f ;txsf] If]qkmn / cfotg kQf
nufpg'xf]; . -pQ/ M 1848 cm2
, 5749.33 cm3
_
22. tLgcf]6f 7f]; uf]nfx¿nfO{ kufn]/ Pp6f 12 cm cw{Jof; ePsf] 7f]; uf]nf agfOPsf] 5 .
olb b'O{cf]6f uf]nfx¿sf] cw{Jof; 6 cm / 8 cm eP t];|f] uf]nfsf] cw{Jof; lgsfNg'xf]; .
-pQ/ M 10cm_