Thiết kế bài giảng hình học 12 (tập 1) phần 2

Chi/dNq 2
MAT NON, MAT TRU, MAT CAU
Phan 1

G\d\ THliu CHLfdNG

I. CAU TAO CHUONG
§ 1. Khai niem vd mat trdn xoay
§2 Mat ciu
On tap chuang II
1. Muc dich cua chuong

• Chuang II nhim cung cap cho hgc sinh nhiing kie'n thiic co ban vd khai nidm cac
khdi trdn xoay trong khdng gian ma chii ye'u la mat ndn, mat tru va mat ciu.
Mat ndn trdn xoay : Day, dudng sinh va dudng trdn day.
Dien tfch xung quanh va dien tich toan phin ciia mat ndn.
Thd tfch ciia khdi ndn trdn xoay
• Mat tru trdn xoay la gi ?
Didn tfch xung quanh va dien tfch toan phan eua mat tru.
The tfch ciia khdi tru trdn xoay
• Mat cau la gi ?
Didn tfch ciia mat ciu.
The tfch ciia khdi cau.

104


I I - MUC TIEU
1. Kien thufc
Nim dugc toan bd kien thiic ca ban trong chuong da neu tren.
- Hidu eac khai niem cac mat trdn xoay: Mat ndn, mat tru va mat cau.

Nim dugc eac cdng thitc tfnh didn tfch, thd tfch ciia cac khdi trdn xoay.
2. KI nang
TinK dugc didn tfch xung quanh, didn tfch toan phan ciia cac hinh trdn xoay.
Tinh dugc thd tfch ciia hinh tru, hinh ndn.
3. Thai do
Hgc xong chuang nay hgc sinh se lien he dugc vdi nhidu va'n dd thuc te sinh ddng,
lien he duge vdi nhung vin dd hinh hgc da hgc d Idp dudi, md ra mdt each nhin
mdi vd hinh hgc. Tii dd, cac em cd thd tu minh sang tao ra nhiing bai toan hoac
nhirng dang toan mdi.
Kit ludn:
Khi hgc xong chuang nay hgc sinh cin lam tdt cac bai tap trong sach giao khda va
lam dugc cae bai kidm tra trong chuang.

105


Phan 2,
ckc BAI SOAN

§1. Khai niem ve mat tron xoay
(tiet 1, 2, 3, 4, 5)
1. MUC Tl!U
1. Kien thufc
HS nim dugc:
1. Khai niem chung vd mat trdn xoay.
2. Hidu va van dung tfnh the tfch binh tru va binh ndn.
3. Dien tfch xung quanh va toan phin ciia mat tru va mat ndn.
2. KT nang
•

Ve thanh thao cac mat tru va mat ndn.

•

Tinh nhanh va chfnh xac didn tfch va the tfch hinh tru va hinh ndn.

•

Phan chia mat tru va mat ndn bing mat phang.

3. Thai do
•

Lien he dugc vdi nhidu van dd thue te trong khdng gian.

•

Cd nhidu sang tao trong hinh hgc.

•

Hiing thii trong hgc tap, tfch cue phat huy tfnh ddc lap trong hgc tap.

n. CHUAN DI CUA GV VA HS

1. Chuan bi cua GV:
• Hinh ve 2.1 de'n 2.12.
• Thudc ke, phin mau,...
106

2. Chuan bi ciia HS :
Dgc bai trudc d nha, cd thd lien he cac phep bie'n hinh da hgc d Idp dudi.
ra. PHAN DHOI TH6I LUONG

Bai dugc chia thanh 5 tiet:
Tiet 1: Tii dau de'n he't phan 1.
Tie't 2: Tie'p theo de'n he't muc 3 phin II
Tidt 3: Tie'p theo de'n he't phin II
Tie't 4: Tie'p theo de'n bet muc 3 phin III
Tie't 3: Tidp theo den bet phin III
IV. TlfN TDiNH DAY HOC
n. DAT VAN D€
Cau hdi 1.
Nhic lai khai nidm hinh ndn va hinh tru da hgc d cap 2.
Cau hdi 2.
Ndu mdt sd hinh ndn va hinh tru trong thuc te.
B. Biil MOI

HOATDQNGl
I. sir TAG THANH MAT TRON XOAY
GV neu cau hoi :

HI. Lg hoa thdng thudng ed phai mat trdn xoay hay khdng?
H2. Chie'c ndn Hue la mat trdn xoay?
107


• GV sir dung hinh 2.1 trong SGK va dat va'n dd:
H3. Hay dgc ten cac hinh d hinh 2.1.

H4. Em hinh dung dugc each lam lg hoa.
H5. Trong cac mat trdn xoay, cd mat nao chic chin la mat phing?
H6. Trong hinh 2.2, khi cit qua A mdt mat phing bat ki ta cd dugc dudng ^ hay
khdng?
H7. Ndu mdt sd hinh anh thuc te vd hinh tru va hinh ndn.

HOATDQNG 2
II. MAT NON TRON XOAY
1. Dinh nghla
• GV eho HS tu phat bidu dinh nghia cua minh va sau dd kdt luan:
Trong mat phdng (P) cho hai dudng thdng d vd A cdt nhau tgi 0 tgo
thdnh gdc nhgn /?. Khi quay mat phdng xung quanh A thi dudng thdng d
sinh ra mdt mat trdn xoay vd dugc ggi Id mat ndn trdn xoay dinh 0
ngUdi ta thudng ggi tat la mat ndn. Dudng thang A ggi Id true, dudng
thdng d ggi Id dudng sinh, gdc 2/3 ggi Id gdc d dinh cua mat ndn dd.
Six dung hinh 2.3 va dat ra eac cau hdi:
H8. Phai chang mat ndn cd gidi ban bdi hai mat phang song song vdi nhau.
H9. Gdc giiia dudng sinh va true ludn ludn khdng ddi.
HIO. Cd mdt phep ddi xitng tam O bid'n mdi diem ciia mat ndn thanh mdi didm
ciia mat ndn.
2. Hinh ndn trdn xoay va khdi ndn tron xoay
• Sit dung hinh 2.4 va md ta:

108


• GV neu dinh nghia ;
Cho tam gidc vudng lOM. Khi quay nd xung quanh mgt cgnh gdc vudng
01 ta dugc mgt tgo thdnh mdt hinh dugc ggi Id hinh ndn trdn xoay. Ta
thudng ggi tdt Id hinh ndn.

• GV cd thd dat cau hdi:
HI 1. Hai tam giac lOM va lOM' ed bing nhau khdng?
HI2. Hay neu tap hgp didm ciia M.
• GV ndu tiep khai niem:
O ggi la dinh cua hinh ndn.
IM ggi la dudng sinh ciia hinh ndn
10 ggi Id dudng cao ciia hinh ndn
Tap hgp diemM la dudng trdn tdm I bdn kinh IM ggi Id ddy ciia hinh ndn.
Phdn hinh ndn bd di mat ddy ggi Id mat xung quanh cua hinh ndn.
H13.10 vudng gdc vdi day. Diing hay sai.
H14. Gdc tao bdi dudng sinh va dudng cao bing bao nhieu Ian gdc d dinh.
• GV ndu dinh nghia khdi ndn trdn xoay:
Khdi ndn trdn xoay Id phdn khdng gian gidi hgn bdi hinh ndn trdn xoay
vd cd hinh ndn.
109


N la diem trong ne'u N thudc khd'i ndn.
N Id diem ngodi niu N khdng thugc khd'i ndn.
H15. Hay neu khai niem dinh, day, dudng sinh, dudng cao ciia khdi ndn.
3. Dien tich xung quanh cua hinh ndn trdn xoay
HI6. Hay ve mdt hinh chdp cd tat ca eac dinh cua day hinh chdp la da giac ndi tie'p
dudng trdn day cia hinh ndn. Dinh cua hinh chdp trimg vdi dinh ciia hinh ndn.

H17. Tam ciia da giac va tam ciia dudng trdn day ludn triing nhau. diing hay sai?
• GV ndu dinh nghla :
Dien tich xung quanh cua hinh ndn trdn xoay la gidi hgn cua dien tich
xung quanh cua hinh chdp deu ndi tiep hinh ndn dd khi sd cgnh ddy tdng
len vd hgn.
HI8. Didn tfch xung quanh ciia hinh chdp ddu ndi tie'p hinh ndn Idn ban hay nho

ban didn tfch xung quanh cua hinh ndn?
H19. Khi nao dien tfch hinh chdp va hinh ndn nhu tren triing nhau?
H20. Nhic lai cdng thiic tfnh dien tfch xung quanh cua hinh ndn.
• GV nhic lai cdng thiie : S

= — pq trong dd q la khoang each tit O de'n mdt

canh p la chu vi day.
H21. Khi n ^^co thi p din de'n sd nao ?
• GV neu dinh If:
Dien tich xung quanh cua hinh ndn bdng nda chu vi ddy nhdn vdi do ddi
dudng sinh.
S^q=7ir/

no


• GV ndu tidp dinh nghla:
Tdng cua dien tich xung quanh vd dien tich ddy ggi Id dien tich todn phdn
cua hinh ndn.
4. The tich cua hinh ndn trdn xoay
• GV neu dinh nghia :
The tich cua hinh ndn trdn.xoay Id gidi hgn cua the tich cUa hinh chdp
diu ndi tie'p hinh ndn dd khi sd cgnh ddy tdng len vd hgn.
H22. Ndu cdng thiic tfnh the tfch hinh chdp.
GV nhic lai V f . = - B h .
•

^

3

H23. Khi sd eanh cua hinh chdp dan tdi cx) thi didn tfch day din de'n sd nao?
• GV ndu cdng thiic :
1
1 9
V„ - - B h ^ - T t r ^ h .

5. Vi du
•GV cho HS tdm tit vf du:

111


Cau a
Hoat ddng cua GV
Cdu hdi 1

Hoat ddng cua HS
Ggi y trd ldi cdu hdi I

Hay chi ra dudng sinh cua hinh Dudng smh la OM.
ndn.
Ggi y trd ldi cdu hdi 2
Cdu hdi 2
IM
, „,,
Tfnh do dai dudng sinh.

1 - OM =

= 2a
sin 30°

Cdu hdi 3
Tinh chu vi day.

Ggi y trd ldi cdu hdi 3
p =2 Ttr = 2Tr.a.

Cdu hdi 4

Tinh dien tfch xung quanh cua Ggi y trd ldi cdu hdi 4
, Sxq = nr\ = 2na^
hinh ndn.

caub
Hoat ddng ciia GV
Cdu hdi 1

Hoat ddng ciia HS
Ggi y trd ldi cdu hdi I

Tfnh dien tfch day.
Cdu hdi 2

S = na^
Ggi y trd ldi cdu hdi 2

Tfnh dudng cao.

Cdu hdi 3

OI = aV3
Ggi y trd ldi cdu hdi 3

TinhV
V-

Thuc hidn ^ 2 trong 4 phiit.
S

112

^^^^'^
3


Hoat ddng cua HS

Hoat ddng ciia GV
Cdu hdi 1

Ggi y trd ldi cdu hdi 1

Tfnh chu vi niia dudng trdn ldn.
Cdu hdi 2

Niia chu vi ciia dudng trdn ldn la chu
vi dudng trdn nhd va bing 27IT

So sanh chu vi ciia dudng trdn Ggi y trd ldi cdu hdi 2
day va niia chu vi dudng trdn ldn. Bang nhau.
Cdu hdi 3

Ggi y trd ldi cdu hdi 3

Tfnh r.

13

Ta cd TTR = 270-. Tit dd r = —
2

HOAT DONG 3
IIL MAT TRU TRON XOAY
1. Djnh nghla
• GV sii dung hinh 2.8 va dat ra cac cau hdi:

113


H24. So sanh OM va O'M'
H25. So sanh OO' va MM'
H26. Hinh OO'M'M la hinh gi?
• GV neu dinh nghia:
Trong mat phdng (P) cho hai dudng thdng A vd I. song song vdi nhau,
cdch nhau mdt khodng r. Khi quay mat phdng (P) xung quanh A thi
dudng thdng I vgch ra mdt mat tru trdn xoay

Ngudi ta thudng ggi tdt

mat tru trdn xoay Id mat tru. Dudng thdng A ggi la tru, dudng thdng I ggi
Id difdng sinh cua mat tru.
Hll. Hay lay mdt sd hinh anh thuc te vd mat tru trdn xoay.
2. Hinh tru trdn xoay
H28. Phai chang mat tru dugc gidi ban bdi hai mat phang song song?
GV neu nhan xet:
Khi ta cit mat tru bdi hai mat phing song song va vudng gdc vdi true thi ta dugc
mdt hinh try trdn xoay.
H29. Hay neu dinh nghia hinh tru trdn xoay.
a) Hinh tru trdn xoay
• GV neu dinh nghla:
Khi quay mdt hinh chit nhdt chung qugnh mot cgnh cua hinh chii nhdt do
ta dugc mdt hinh tru trdn xoay.
Cgnh diing de quay ggi la true.
Cgnh ddi dien ggi Id dudng sinh
Hai cgnh cdn lgi Id hai bdn kinh ddy cua hai mat ddy.

114


H30. Hai day cua hinh tru la hinh gi?
H31. Khi cit hinh tru bdi mdt mat phing song song vdi hai day ta dugc hinh gi?
H32. Khi cat hinh tru bdi mat phing di qua tmc ta dugc hmh gi?

H33. Hay md ta mat xung quanh cua mat tru.
H34. Hay ndu chidu cao cua hinh tru.
H35. So sanh dudng cao va dudng sinh.
H36. So sanh hai day.
b) Khdi tru trdn xoay

GV ndu cac khai niem:
- Khdi tru la gi ?
- Didm ngoai va didm trong eiia mat tru.
- Mat day, dudng sinh, dudng cao ciia khdi tru.
3. Dien tich xung quanh cua hinh tru trdn xoay
a) Hinh ldng tru ndi tie'p hinh tru:

115


• GV neu khai niem lang trii ndi tie'p hinh tru trdn xoay :
Mdt hinh ldng tru ggi Id ndi tie'p hinh tru niu hai ddy ciia hinh ldng tru
ngi tiip hai dudng trdn ddy ciia hinh tru.
H37. Neu mdt sd vf du vd hinh anh ciia dinh nghla trdn.
• GV neu dinh nghia :
Dien tich xung quanh mdt hinh tru trdn xoay Id gidi hgn cUa dien tich
xung quanh hinh ldng tru ndi tiep hinh tru dd khi sd'cgnh cua da gidc ddy
ddn ra vd cue.
b) Cdng thuc tinh dien tich xung quanh ciia hinh tru
H38. Hay nhic lai cdng thiie didn tfch xung quanh cua hinh lang tru.
H39. Hay nhic lai cdng thiic dien tfch xung quanh cua hinh lang tru ddu.
• GV nhic lai cdng thiic dien tfch xung quanh ciia hinh lang tru ddu :
Sj^q = ph (p lachu vi day, h la dudng cao).
• GV neu dinh nghla :

116


Dim tich xung quanh cua hinh tru Id gidi hgn cua dien tich xung quanh
cua hinh ldng tru deu ndi tie'p hinh tru dd khi sd cgnh ddy cua ldng tru

ddn ra vd cue.

• GV ndu khai nidm dien tfch toan phin :

• GV neu hinh bieu didn didn tfch toan phin ciia mdt hinh tru:

H40. hay chi ra cac phin cd :
- Dd dai bang nhau .
Cd didn tfch bing nhau
d hai hinh trdn
4. The tich khdi tru trdn xoay
a) Dinh nghia:
The tich khdi tru trdn xoay la gidi hgn cua the tich khdi ldng tru diu ndi
tiep khdi tru dd khi cgnh ddy tdng len vd hgn.
117


b) Cdng thdc:
GV neu cdng thiic :
V = Bh

Thuc hien ^ 3 trong 4 phut.

A'
B'
D'
Hoat ddng cua GV
Cdu hdi 1

C

Hoat ddng ciia HS
Ggi y trd ldi cdu hdi I

Tfnh ban kfnh ciia dudng trdn day
aV2
cua hinh tru
r=
2
Cdu hdi 2
Ggi y trd ldi cdu hdi 2
Tinh chu vi dudng trdn day.
p - IKX = 2n
= Trav2 .

Cdu hdi 3

Ggi y trd ldi cdu hdi 3

Tfnh dien tich xung quanh.
Sxq = Pl = 7taA/^.a = Tia^4i.

118


5. Vi du
GV cho HS neu tdm tit bai toan, ve hinh.
l^^-^
.

/Ok

^ ^ . - ^

'

N

1

ji

a

— 1-/

1

'''"

y

1 c
''

*^

y

cau a.
Hoat ddng cua GV

Cdu hdi I

Hoat ddng cua HS
Ggi y trd ldi cdu hdi 1

Hay chi ra va tfnh ban kfnh day
r= AI=^
cua hinh tru.
2
Cdu hdi 2
Hay chi ra va tfnh dudng sinh cua
hinh tru.
Cdu hdi 3

Ggi y trd ldi cdu hdi 2
I = AD = a.

Ggi y trd ldi cdu hdi 3

Tinh dien tfch xung quanh.
Svn
xq = pi-l = 27t —a
2 = 7ca

Caub.
Hoat ddng cua GV
Cdu hdi I

Hoat ddng ciia HS
Ggi y trd ldi cdu hdi I

Hay chi ra va tfnh ban kfnh day
AT
^
ciia hinh tru.
r = AI = —
2
119


Cdu hdi 2

Ggi y trd ldi cdu hdi 2

Hay cbl ra va tfnh dudng cao ciia h = IH = a.
hinh tru.
Cdu hdi 3

Ggi y trd ldi cdu hdi 3

Tinh thd tfch xung quanh.

2

V = Tir^h = Tt

[ij

1

1
2
= —Tia

4

HOAT DONG 4
TOM TflT Bfll Hpc
1. Trong mat phang (P) cho hai dudng thing d va A cit nhau tai O tao thanh gdc
nhgn p. Khi quay mat phing xung quanh A thi dudng thing d sinh ra mdt mat trdn
xoay va dugc ggi la mat ndn trdn xoay dinh O ngudi ta thudng ggi tit la mat non.
Dudng thing A ggi la true, dudng thing d ggi la dudng sinh, gdc 2(3 ggi la gdc d
dinh cua mat ndn dd.
2. Cho tam giac vudng lOM. Khi quay nd xung quanh mdt canh gdc vudng 01 ta
tao thanh mdt hinh duge ggi la hinh ndn trdn xoay. Ta thudng ggi tit la hinh ndn.
O ggi la dinh ciia hinh ndn.
IM ggi la dudng sinh ciia hinh ndn.
IO ggi la dudng cao cua hinh ndn.
Tap hgp didm M la dudng trdn tam I ban kfnh IM ggi la day ciia hinh ndn.
Phan hinh ndn bd di mat day ggi la mat xung quanh cua hinh ndn.
3. Khdi ndn trdn xoay la phan khdng gian gidi ban bdi hinh ndn trdn xoay va ca
hinh ndn.
N la didm trong ne'u N thudc khdi ndn.
N la didm ngoai ne'u N khdng thugc khdi ndn.

120


4. Didn tfch xung quanh cua hinh ndn bing nua chu vi day nhan vdi do dai dudng
sinh. S^q =: Tir/

5.Tdng cua dien tfch xung quanh va dien tfch day ggi la dien tfch toan phin cua
hinh ndn.
6. The tieh ciia hinh ndn trdn xoay la gidi ban cua thd tfch ciia hinh chdp ddu ndi
tidp hinh ndn dd khi sd canh day tang Ien vd ban.
1
1 9
V = - B h = -Ttr^h.
" 3
3
7. Trong mat phing (P) cho hai dudng thing A va 1. song song vdi nhau, cich nhau
mdt khoang r. Khi quay mat phang (P) xung quanh A thi dudng thing 1 vach ra
mdt mat true trdn xoay

Ngudi ta thudng ggi tit mat tru trdn xoay la mat tru.

Dudng thing A ggi la true, dudng thing 1 ggi la dudng sinh ciia mat tru.
8. Khi quay mdt hinh chu: nhat chung quanh mdt eanh ciia hinh chii nhat dd ta
dugc mdt hinh tru trdn xoay.
Canh diing dd quay ggi la true.
Canh ddi didn ggi la dudng sinh
Hai canh cdn lai la hai ban kfnh day cua hai mat day.
9. Mdt hinh lang tru ggi la ndi tidp hinh tru nd'u hai day ciia hinh lang tru ndi tidp
hai dudng trdn day ciia hinh tru.
Didn tfch xung quanh mdt hinh tru trdn xoay la gidi ban eua dien tfch xung quanh
hinh lang tru ndi tie'p hinh tru dd khi sd canh ciia da giac day din ra vd cite.
10. Didn tfch xung quanh eiia hinh tru la gidi ban ciia dien tich xung quanh cua
hinh lang tru ddu ndi tie'p hinh tru dd khi sd eanh day ciia lang tru din ra vd cue.
S„„ = 27rr/
Aq

11. Didn tfch toan phin :
^tp - Sxq + S(j
12. Thd tfch khdi tru trdn xoay la gidi han eua thd tfch khdi lang tru ddu ndi tiep
khdi tru dd khi canh day tang Idn vd ban.
Cdng thiic :

V = Bh
121


HOATDQNG 3
MQT SO CflU H6r TR^C NGHl|M
Hay didn diing (D) sai (S) vao cac khang dinh sau :
Cdu 1.

(b) Mat ndn trdn xoay va hinh ndn la nhu nhau.

D
D

(c) Hinh ndn la mdt phin ciia mat ndn.

D

(d) Ca ba khang dinh trdn ddu sai.

•

(a) Hinh ndn va hinh chdp la nhu nhau.

Trd ldi.
a

b

c

d

S

S

S

D

Cdu 2.
(a) Mat ndn trdn xoay la mdt hinh cd tam ddi xiing.

D

(b) Mat ndn trdn xoay khi bi cit bdi mdt mat phang vudng gdc vdi true

(e) Hinh ndn cd mdt true ddi xumg.

D
D

(d) Ca ba khang dinh trdn ddu sai.

n

ta cd the duge mdt hinh ndn.

Trd ldi.
a

b

c

d

D

D

D

S

122


Cdu 3.
(a) Mat tru trdn xoay khdng cd gidi ban.

[_}

(b) Hinh tru cd gidi ban.

U

(c) Khi cit mdt hinh tru bdi mdt mat phang // true ta dugc hinh chii nhat.

[J

(d) Ca ba khing dinh trdn ddu sai.

Ll

Trd ldi.

a

b

c

d

D

D

D

s

Cdu 4.
(a) Mat tru trdn xoay khi gidi han bdi hai mat phang
song song ta dugc hinh tru.

D

(b) Mat tru trdn xoay khi gidi han bdi hai mat phing
vudng gdc vdi true ta dugc hinh tru.

D

(c) Khi cit mdt hinh tru bdi mdt mat phang ± true ta dugc hinh trdn.

•

(d) Ca ba khang dinh trdn ddu sai.

D

Trd ldi.

a

b

c

d

D

D

D

S

Chgn kh^ng djnh diing trong cac cau sau:
Cdu 5. Cho hinh chdp ndi tidp mdt hinh ndn


(a) Hai hinh chdp va hinh ndn cd dudng cao trung nhau;
(b) Thd tfch hinh chdp va thd tfch hinh ndn bing nhau.
(c) Thd tfch hinh chdp Idn ban the tfch hinh ndn.
(d) Ca ba y trdn ddu diing.
Trd ldi. (a).
Cdu 6. Cho hinh chdp luc giac ddu canh day la 2v3 ndi tidp mdt hinh ndn co
dudng cao la 3.
S

Dudng cao ke tii S cua mdi mat bdn ciia hinh chdp la :

(a)2VlO;
(c)

(b)Vio

10
(d)10

Trdldi. (b).
Cdu 7 Cho hinh chdp luc giac ddu canh day la 2>/3 ndi tidp mdt hinh ndn co
dudng cao la 3.

124


Didn tfch xuhg quanh ciia hinh chdp la :
(a)6V30;

(b) V30

(c)4V30;

(d)5V30

Trdldi. (a).
Cdu 8. Cho hinh chdp luc giac ddu canh day la 2V3 ndi tidp mdt hinh ndn cd
dudng cao la 3.

Ban kfnh dudng trdn day la:
(a) 2yf3;

(b) 2V6

,. 2V3
(0—;

(d) V3.

Trdldi. (a).
Cdu 9. Cho hinh chdp luc giac ddu canh day la 2V3 ndi tie'p mdt hinh ndn cd
dudng cao la 3.

125


Dudng sinh la:
(a)2V3;

(b) 2V6

,- 2V3

(d) V3.

Trdldi. (b).
Cdu 10. Cho hinh chdp luc giac ddu canh day la 2>/3 ndi tiep mdt hinh ndn cd
dudng cao la 3.

Didn tfch xung quanh cua hinh ndn la
(a) llnyfl;

(b) 24TIV2

(c) 6T1V2 ;

(d) 48TI^/2

Trdldi. (d).

Cdu 11. Cho hinh chdp luc giac ddu canh day la 2>/3 ndi tidp mat hinh ndn cd
dudng cao la 3

126


Didn tfch toan phin ciia hinh ndn la:
(a) I2T1V2 + 1271;

(b) 24TIV2 + 127I

(c) 6TiV2 + 127r;

(d)

48TI^+12TI.

Trdldi. (d).
Cdu 12. Cho hinh chdp luc giac ddu canh day la 2V3 ndi tie]
tiep mdt hinh ndn cd
dudng cag la 3.

Thd tfch ciia hinh ndn la:
(a) 1271;

(b) 671

(c) 871;

(d) IOTI.

Trdldi. (a).
Cdu 13. Cho hinh lang tru luc giac ddu eanh day la 2V3 ndi tie'p mdt hinh tru cd
dudng cao la 3.

127


A'

, /-

->

Didn tfch xung quanh ciia hinh lang tru la:
(a)36V3;

(b) 16V3

(c)46V3;

(d)26V3

Trd ldi. (a).
Cdu 14. Cho hinh lang tru luc giac ddu eanh day la 2V3 ndi tidp mdt hinh tru co
dudng cao la 3.
A

A'

/
D'
E'

Dudng sinh cua hinh tru la
(a)2V3;

(b)3V3

(c)3;

(d)6.

Trd ldi. (c).

128