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

TRAN VINH

nINn H
NANG CAO
TAP HAI

NHA XUAT BAN HA NOI

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TRAN VINH

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THIET KE BAI GIANG

H I N H HOC 12
TAP 2 - NANG CAO

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NHA XUAT BAN HA NOI

ChiroNq 11
MAT CAU, I^IAT TRU, MAT NON
Pliun 1
G\6\ THIEU CHLfCNG

I. CAU TAO CHUONG
§1. Mat cau, khd'i cau
§2. Khai niem vl mat trdn xoay
§3. Mat tru, hinh tru va khdi tru
§4. Mat ndn hinh ndn va khd'i ndn
On tap chuong II
Muc dich ciia chuong
Chuong II nham cung cap cho hpc sinh nhiJng kiln thuc co ban vl khai niem cac
khdi trdn xoay trong khong gian ma chu ylu la mat ndn, mat tru va mat cau.
• Mat cau la gi. Su xac dinh mat cau. Dudng trdn Idn ciia mat cau.
Dien tich cua mat cau.
Thi tich ciia mat cau.
• Mat tru trdn xoay la gi.
Dien tfch xung quanh va dien tich toan phan ciia mat tru.
Thi tich ciia khdi tru
• Mat ndn trdn xoay : Day, dudng sinh va dudng trdn day.
Dien ti'ch xung quanh va dien tich toan phan ciia mat ndn.
The tich ciia khdi ndn


II. MUC TIEU
1. Kien thuc
Nam dupe loan bp kien ihiic co ban trong chuong da neu tren.
1 lilu cac khai niem cac mat trdn xoay: Mat cau, mat tru va mat ndn.
Nam dupe cac cong thiic tinh dien tich, the tich ciia cac mat trdn xoay.

2. KT nang
Tinh dupe dien tich xung quanh, dien tfch toan phan ciia cac hinh trdn xoay.
Tfnh dupe thi tfch ciia khdi cau, khdi tru, khdi ndn.
3. Thai dp
Hpc xong chuong nay hpc sinh se lien he dupe vdi nhilu van dl thuc t l sinh dong,
lien he dupe vdi nhiing van dl hinh hpc da hpc d lop dudi, md ra mot each nhin
mdi vl hinh hpc, dac biet la van dl hlnh hpc khong gian. TCr dd, cac em cd thi tu
minh sang tao ra nhirng bai toan hoac nhirng dang toan mdi.
Kit luan:
Khi hpc xong chuong nay hpc sinh can lam tdt cac bai tap trong sach giao khoa va
lam dupe cac bai kilm tra trong chuong II.


Phun 2
CAC PAI SCAN

(TI^P THEO)

§3. Mat tru, hinh tru, khoi tru
(tiet 6, 7)
1. MUC TIEU

1. Kien thdc
HS nam duoc:
1. Khai niem chung vl ma tru.
2. Diem thudc mat tru , dilm d trong va dilm d ngoai mat tru.
3. Giao ciia mat tru va mat phang.
4. Hinh tru la gi, cac khai niem ca ban vl hinh tru, dien tich xung quanh, dien tfch
toan phan cua hinh tru.
5. Khd'i tru va the tfch ciia khd'i tru.

2. KT nang
•

Ve thanh thao cac mat hinh tru.

•

Xac dinh mat tru, hinh tru, khdi tru.

•

Phan biet duoc ba khai niem tren.

•

Tfnh dupe thi tfch va dien tfch ciia hinh tru va khdi tru.

3. Thai dp
•

Lien he dupe vdi nhilu van dl thuc t l trong khong gian.

•

Cd nhilu sang tao trong hinh hpc.

•

filing thii trong hpc tap, tich cue phat huy tinh dpc lap trong hpc tap.

II. aiU:V\ BI CUA CV VA n&
1. C h u a n bi cua GV:
• ITinh \e 43 den 47.
• Thudc kc. pha'n mau, ...
2. Chuan bj cua HS :
Dpc bai trudc d nha, cd thi lien he cac hlnh khdng gian, hlnh tru da hpc d Idp
dudi \k trong thuc tl.
III. PHAN DUOI THOI LUONG
Bai dupe chia thanh 2 tilt :
Tiet 1: Tir dau din hit muc 2
Tilt 2: Tiep theo din hit.
IV. TIEN TDlNH DAY HOC
n . DHT VHN D€
Cau hdi 1.
Hay neu dinh nghia hinh trdn xoay.
Cau hdi 2.
Neu cac dac dilm chung cua hinh trdn xoay?
R. BHi MOI

HOATDONCl
1. Djnh nghTa mat tru
GV neu cau hdi :
HI. Em hay neu khai niem hinh lang tru.


H2. Banh xe may lu cd la hinh trdn xoay hay khdng? Neu cac dac dilm ciia nd?
• GV neu dinh nghia :
Mat Iron xoay sinh b(fi dudng llidng I khi quay quanh dudng thdng A
song song vdi I dugc ggi Id mat tru iron xoay (hoac vdn idl Id mat tru).

GV sir dung hinh 42 va dua ra cac cau hdi
A

H3. Mat tru cd day hay khong?
H4. A va / cd quan he nhu thi nao?
H5. So sanh khoang each giiJa A va /, A va /,?
• GV neu cac khai niem co ban ciia hinh tru:
A ggi Id true cua mat Iru vd I ggi Id dudng sinh cua mat tru, R ggi Id
bdn kinh ciia mat tru.
H6. Khi nao dilm M d ngoai mat tru?
H7. Hay neu khai niem ban kfnh ciia mat tru.
H8. Em hay dinh nghia mat tru theo ngdn ngir tap hop.
H9. Nlu mdt dilm thudc mat tru thi nd thudc mot dudng sinh nao dd. Diing hay sai?
HIO. Hay neu mdi quan he giira cac dudng sinh khac nhau ciia mat tru.
• GV neu eac chii y:
a) Mat irii ndi tren Id lap hgp Id'l cd nhung diem M cdch dudng thdng A
cd dinh mgt khodng R khdng ddi.


b) Ne'u ;V/| Id mdt diem bdt ki ndm tren mat Iru thi dudng thdng /| di
qua A/, vd song song vdi A se ndm tren mdl tru dd (vi mgi diem ciia /|
deu cdch A mdl khodng R). NliU vdy, cd the xem mat tru sinh bdi dudng
thdng /, , ndi cdch khdc, dudng thdng /, cung Id mdl dudng sinh ciia mat
tru.
Thuc hien -M" trong 5'
a)
Hoat ddng ciia HS

Hoat ddng ciia GV
Cdu hdi 1

Ggi y trd Idi cdu hdi 1

Hay neu khai niem dudng sinh
ciia mat tru?
Cdu hdi 2

HS tu neu.

Ggi y trd Idi cdu hdi 2

Tim giao ciia T va mat tru trong
Giao ciia T va A la hai dudng sinh ddi
trudng hop nay.
xung vdi nhau qua A.
b)
Hoat ddng ciia GV
Cdu hdi 1

Hoat ddng ciia HS
Ggi y trd Idi cdu hdi 1

Gpi d la khoang each tir A den Cd 3 kha nang:
(P). Hay cho bilt cac kha nang cd d < R ; d = R v a d > R .
thi xay ra.
Cdu hdi 2

Ggi y trd Idi cdu hdi 2
Tim giao ciia T \a mat tru trong
+ Nlu d > R thi giao la tap rdng.

trudng hop nay.
+ Nlu d = R thi giao la mot dudng
sinh.
+ Nlu 0 < d < R giao la mot cap
dudng sinh.

c)

i


Hoat ddng ciia HS

Hoat ddng cua GV

Ggi y trd Idi cdu hdi 1

Cdu hdi 1
Hay neu mdi quan he ciia cac

Cac dudng sinh vudng gdc vdi A.

dudng sinh va A.
Cdu hdi 2

Ggi y trd Idi cdu hdi 2

Tim giao cua T va mat tru trong
trudng hop nay.

iP) 1 A : giao la dudng trdn cd ban
kfnh R.

HOATDONC 2
2. Hinh tru va khoi tru
• GV sir dung hinh ve 43 va neu cac cau hdi :

H l l . Khi cat mat tru bdi hai mat phang ta dupe hinh gi ?
HI2. Neu mdt vai hinh anh thuc tlciia viec cat tren?
• GV neu dinh nghia :
Phdn mat Iru T nam giUa hai mat phdng (P) vd (P') cimg vdi hai hinh
trdn xdc dinh bdi ( )^) vd ( '^') dugc ggi Id hinh iru.
• GV neu cac cau hdi


HI3. Neu khai niem day ciia hinh tru.
HI4. Neu khai niem chilu cao ciia hinh tru.
HI5. Neu khai niem true ciia hinh tru.
• GV neu cac khai niem dilm nam trong, nam tren va nam ngoai hinh tru. Gpi R
la ban kfnh cua hlnh tru, d la khoang each tir true A din dudng thang m // d. Hay
diln vao bang sau:
d

3

R

5

3

7

9

6

8

Tren

Vi trf
• GV neu dinh nghia

Hinh tru ciing vdi phdn ben Irong ciia nd dugc ggi Id khdi tru xdc
dinh bdi hinh Iru dd.
HI6. Mpi diem thuoc mat tru diu thudc hinh tru . Diing hay sai?

• Thuc hien vi du 1 trong 5'. GV sir dung hinh 44.
D

B

Hoat ddng cua GV
Cdu hdi 1

c
Hoat ddng ciia HS
GrA y trd Idi cdu hdi 1

Gpi C D' lan lupt la hinh chilu ABCD' la hinh chu nhat.
ciia C, D tren mat day chiia AB
thi AfiC'D'la hinh gi?
Cdu hdi 2
Hay tfnh AB.

10

Ggi y trd Idi cdu hdi 2
Ta cd AC = 2/?, BC' = 4/?^ -- A 5 - =


BC^ - CC^ = AB^ - R^
Suy ra : 2A/i^ = 5/?^ hay AB =

'^^

HOATDONC 3
3. Dien tich hinh tru va the tich khoi tru
• GV neu khai niem hinh lang tru noi tilp hinh tru.
• GV neu dinh nghia :
Dien tich xung quanh ciia hinh Iru Id gidi hgn ciia dien tich xung quanh
ciia hinh Idng tru deu ndi Hep khi sd cgnh ddy idng len vo hgn. The tich
ciia khdi iru Id gidi hgn cua the lich ciia khdi tdng tru deu ndi lie'p khi sd
cgnh ddy tdng len vd hgn.
HI7. So sanh dien tfch xung quanh ciia hinh tru va hinh lang tru noi tiep.
• GV neu dinh If:
Dien lich xung quanh ciia hinh tru bdng chu vi ddy nhdn vdi chieu cao.
The lich ciia khd'i Iru bdng dien tich ddy nhdn vcri chieu cao
HI8. Chiing minh y thir nhat ciia dinh If.

• Thuc hien vf du 2 trong 5' GV sir dung hinh 46.
•0^-

.0',

1)
Hoat ddng ciia GV
Cdu hoi 1

Hoat ddng eiia HS
Ggi y trd loi cdu hdi 1

11


Tfnh dien tfch xung quanh ciia

4;r/^-

mat tru.

Ggi y trd loi cdu hdi 2

Cdu hdi 2
Tfnh dien tfch ciia mat cau.

AnR^

2)
Hoat ddng ciia GV

Hoat ddng ciia HS

Cdu hdi 1

Ggi y trd Idi cdu hdi 1

Tfnh dien tfch toan phan ciia mat

4nR^+ 2nP?= ^nR^

tru.

Ggi y trd Idi cdu hdi 2

Cdu hdi 2

2
Dien tfch mat cau bane — dien tfch
3
toan phan ciia hinh tru.

So sanh

3)
Hoat ddng ciia GV

Hoat ddng ciia HS

Cdu hdi 1

Ggi y trd Idi cdu hdi 1

Tinh thi tich ciia khd'i tru.
Cdu hdi 2

Vj= nR^.2R = 2K R^
Ggi y trd Idi cdu hdi 2

Tinh thi tich ciia khdi cau.

4

^

T,

3

HOATDONC 4
TOM TfiT B^l HOC
1. Mat trdn xoay sinh bdi dudng thdng / khi quay quanh dudng thang A song
song vdi 1 dupe gpi la mat tru trdn xoay (hoac van tat la mat tru).

12


A gpi la true ciia mat tru va / goi la dudng sinh ciia mat tru, R gpi la ban
kinh ciia mat tru.
2. Phan mat tru T nam giira hai mat phang (P) va (F) ciing vdi hai hinh trdn xac

dinh bdi C ^ ) va CW') dupe gpi la hinh tru.
3. Hinh tru ciing vdi phan ben trong ciia nd dupe gpi la khd'i tru xac dinh bdi hinh
tru dd.
4. Dien lich xung quanh ciia hlnh tru la gidi han ciia dien tfch xung quanh ciia
hinh lang tru diu ndi tilp khi sd canh day tang len vd han. Thi tich ciia khdi tru la
gidi han ciia thi tfch ciia khd'i lang tru diu ndi tilp khi sd canh day tang len vo
ban.
5. Dien tfch xung quanh ciia hinh tru bang chu vi day nhan vdi chilu cao.
Thi tfch ciia khdi tru bang dien tfch day nhan vdi chilu cao.

HOATDONC

5

MOT SO C^U HOI TRHC NGHIEM
Hay diln dung (D) sai (S) vao cac khang dinh sau :
Cdu 1.
(a) Mot mat phang cat hinh tru thi cat theo mdt dudng trdn

|_|

(b) Mdt mat phang cat hinh tru thi cat theo mdt hinh chir nhat

|_J

(c) Mot mat phang // vdi true cat hlnh tru thi eat theo mdt hlnh chir nhat

[J

(d) Mot mat phang J_ vdi true cat hinh Iru thi cat theo mdt dudng trdn

[_J

Trd Idi.
a

b

c

d

S

S

D

D

Cdu 2.

13


D

(a) Mat tru la hinh tru
(b) Mot doan thang quay quanh mot dudng thang song song vdi nd

D

thi dupe mot hinh tru.
(c) Tinh tiln mot hinh trdn theo mot vecto cd gia song song vdi
duong thang Niiong gdc vdi mat phing chiia dudng trdn ta dupe mot hinh tru.

D

(d) Ca ba khang dinh tren diu sai

n

Trd Idi.
a

b

c

d

S

D

D

S

Cdu 3. Gpi d la khoang each tir true A ciia hinh tru T den mat phang (P). R la ban

kfnh.
(a) d > R thi (P) cdt (T)
(b) d < R thi (P) cat (T)
(c) d = R thi (P) cat (T)
(d) Ca ba khang dinh tren diu sai

u
D
D

Trd Idi.
a

b

c

d

S

D

D

S

Cdu 4. Gpi d la khoang each tir true A ciia hinh tru T din mat dudng thdng / // A.
R la ban kfnh.

(b) d < R thi / ndm trong vdi (T)

D
D

(d) Ca ba khdng dinh tren diu sai

n

(a) d > R thi / ndm ngoai vdi (T)

14


Trd Idi.
a

b

c

d

S

S

D

S

Chpn khang dinh dung trong cac cau sau:
Cdu 5. Gpi d la khoang each tir true A ciia mat tru T den mat phang (P). R la ban
kfnh ciia mat tru.
Diln vao chd trdng sau :
d

3

4

5

5

R

5

4

4

8

Vi tri tuang
ddi cua (P) vd
T
Cdu 6. Gpi d la khoang each tir true A ciia mat tru T din dudng thdng m. R la ban
kfnh ciia mat tru.

Diln vao cho trdng sau :
d

3

4

5

5

r

5

4

4

8

Vi tri tuang
ddi ciia m vd
T
Cdu 7. Cho hinh lang tru luc giac diu canh day la 2v3 noi tiep mot hinh tru cd
dudng cao la 3

15

c
D'

Dien tich xung quanh ciia hinh lang tru la:
(a) 36 V3 ;

(b)16 V3

(c)46V3;

(d)26V3,

Trd Idi. (a).
Cdu 8. Cho hinh lang tru luc giac diu canh day la 2\/3 ndi tilp mot hinh tru co
dudng cao la 3

A'

->

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

(b)3V3

(c)3;

(d)6.

Trd Idi. (c).

16


Cdu 9. Cho hinh lang tru luc giac diu canh day la 2%/3 noi tiep mot hinh tru cd
dudng cao la 3

B'

A'

, ^-

E'

Ban kfnh day ciia hinh tru la :
(a)r = 2 V 3 ;

(b) r = 3 V3

(c) r = 3 ;

(d) r - 6.

Trdldi. (a).
Cdu 10. Cho hinh lang tru luc giac diu canh day la 2v3 ndi tiep mot hinh tru cd
dudng cao la 3
A

1

B

'

1 A'

'

!

r*
D'

Dien tich xung quanh cua hinh tru la:

(7


(a) 1271x3;

(b) 147tV3

(c)127r;

(d) 1471.

Trd Idi. (a).
Cdu 11. Cho hinh lang tru luc giac diu canh day la 2V3 ndi tiep mot hinh tru co
dudng cao la 3

A

A' _ _

Dien tfch toan phan ciia hinh tru la

:

(a) 1 2;iV3 ;

(b)207r^/3

(c)127x:

(d) 14;T.

Trdldi. (b).
Cdu 12. Cho hinh lang tru luc giac diu canh day la 2v3 noi tilp mdt hinh tru co
dudng cao la 3

18


Thi tfch cua hinh tru la :
(a)97rV3 ;

(b) IO71V3

(c) 1271;

(d) 147t.

Trd Idi. ia).

HOATDONC 6

HCrOTNG DflN Bfil T6P SGK
Bai 11. Hudng ddn. Sir dung tfnh chat ddi xiing cua mdt hinh.
• De chiing minh hinh trdn xoay H cd true ddi xiirng ta can chiing minh :
Lay mot dilm M e Qjfva gpi M' la dilm ddi xiing cua M qua A thi MM' la dudng
kfnh cua dudng trdn C"^) nen M'e d%f Tir dd suy ra A la true ddi xung ciia hinh

Bai 12. Hudng ddn. Dua vao tfnh chat va dinh nghia cua mat tru.
Ddp sd. a) Hinh tru.

b) Khd'i tru.

Bai 13. Hirdng ddn. Dua vao tfnh chat ciia hinh tru.
A

Nlu dilm M cd hinh chilu M' ndm tren (O ; 7?)
Chiing minh MM' 11 A va khoang each tir M tdi A bang M'O = R.
Bai 14. Hudng ddn. Hay chiing minh dudng thdng dd luon each dudng thdng da
cho mot khoang khong ddi R.
19


Xem hinh ve. GV va HS tu chiing minh.
Bai 15. Hirdng ddn. Chung minh mat tru dd cd ban kfnh la R va dudng sinh 2R.

Ddp sd.
a) S,^ = 2nR.lR = 4nR^ ; Sjp = 5„^ + 25^^, = 4nR^ + 2KR^
h)V = 7:R~.2R = 2nR^
c) V^j

=2R'.2R^4R^

Bai 16. Hudng ddn.

20

= 6nR-


a) S^^^
= 27tR.RS
xq

= 243nR^

h)S = S^„ +2S^,^., = 2yf3Klf + 27tR^ = 2iS

+ \)KR-

/?V3

c)0'H = -

§4. Mat non, h i n h n o n va khoi n o n
(tiet 8, 9)

I. MUC TIEU

1. Kien thiic
HS ndm duoc:
1. Khai niem mat ndn, hinh ndn.
2. Hiiu va van dung tfnh thi tfch khd'i ndn.
3. Dien tfch xung quanh va toan phdn ciia mat tru va mat ndn.
2. KT nang
•

Ve thanh thao mat ndn

•

Tfnh nhanh va chfnh xac dien tfch va thi tfch mat ndn, khd'i ndn.

•

Phan chia mat ndn bdng mat phang.

3. Thai do
•

Lien he dupe vdi nhilu van dl thuc t l trong khdng gian.

•

Cd nhilu sang tao trong hinh hpc.

•

Hung thii trong hpc tap, tfch cue phat huy tfnh dpc lap trong hpc tap.

11. CHUAN Bl CUA GV VA H&
1. Chuan bi cua GV:
21


• Hinh ve 49 den 53
• Thudc ke, phan mau, ...
2. Chuain bj ciia HS :
Dpc bai trudc d nha, cd thi lien he cac phep bien hinh da hpc d Idp dudi.
III. PHAN PHOI THOI LUONG
Bai dupe chia thanh 2 tilt :
Tilt 1: Tir dau den hit muc 2.
Tiet 2: Tilp theo den hit.
IV. TIEN TPINH DAY HOC
n. DRT VnN l}€
Cau hdi 1.
Nhdc lai khai niem hinh ndn da hpc THCS
Cau hdi 2.
Neu mot sd hinh ndn trong thuc tl.
a. Bni MOI

HOATDONCl
1. Djnh nghTa m a t ndn
GV neu cau hdi:
HI. Chile ndn Hue la mat trdn xoay?
• GV neu dinh nghia :
Mat Iron xoay sinh bdi dudng thdng I khi quay quanh A ggi Id mat ndn

trdn xoay (hay vdn tdl la mat ndn).

22


A ggi Id true ciia mat ndn: I ggi Id dudng sinh ciia mdl non
O ggi Id dinh cua mat ndn : Gdc la ggi Id gdc d dinh ciia mat ndn.
GV sir dung hinh 49 va dat cac cau hdi:
A

H2. Hinh ndn cd vd sd dudng sinh. Diing hay sai?
H3. Cac dudng sinh cua mat ndn ddng quy. Diing hay sai?
H4. Dinh ciia hinh ndn thudc true ciia no. Diing hay sai?
• Thuc hien ^^

1 trong 5'.

a)
Hoat ddng ciia GV
Cdu hdi 1

Hoat ddng ciia HS
Ggi y trd Idi cdu hdi 1

Khi cdt mat ndn bdi mot mat phdng La 2 dudng sinh.
ta dupe hai dudng thang m va n. m
va n la dudng gi ciia hlnh ndn ?

23