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

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

ChiroNq 11

MAT CAU, I^IAT T R U , MAT NON

P l i u n 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

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

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 G V :

• 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

1 Djnh nghTa mat tru

GV neu cau hdi :

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 GV

Cdu hdi 1

Hay neu khai niem dudng sinh

ciia mat tru?

Cdu hdi 2

Tim giao ciia T va mat tru trong

trudng hop nay

Hoat ddng ciia HS

Ggi y trd Idi cdu hdi 1

HS tu neu

Ggi y trd Idi cdu hdi 2

Giao ciia T va A la hai dudng sinh ddi xung vdi nhau qua A

b)

Hoat ddng ciia GV

Cdu hdi 1

Gpi d la khoang each tir A den

(P) Hay cho bilt cac kha nang cd

thi xay ra

Cdu hdi 2

Tim giao ciia T \a mat tru trong

trudng hop nay

Ggi y trd Idi cdu hdi 2

+ Nlu d > R thi giao la tap rdng

+ Nlu d = R thi giao la mot dudng

sinh

+ Nlu 0 < d < R giao la mot cap

dudng sinh

c)

Tim giao cua T va mat tru trong

trudng hop nay

Hoat ddng ciia HS

Ggi y trd Idi cdu hdi 1

Cac dudng sinh vudng gdc vdi A

Ggi y trd Idi cdu hdi 2

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:

• 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

Gpi C D' lan lupt la hinh chilu

ciia C, D tren mat day chiia AB

thi AfiC'D'la hinh gi?

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)

Cdu hoi 1 Ggi y trd loi cdu hdi 1

11

Tfnh dien tfch xung quanh ciia

3 toan phan ciia hinh tru

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)

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

(a) Mat tru la hinh tru

(b) Mot doan thang quay quanh mot dudng thang song song vdi nd

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) Ca ba khang dinh tren diu sai

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

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

(d) Ca ba khdng dinh tren diu sai

D

D

n

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 :

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 :

Cdu 8 Cho hinh lang tru luc giac diu canh day la 2\/3 ndi tilp mot hinh tru co

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

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

Thi tfch cua hinh tru la :

(a)97rV3 ;

(c) 1271;

Trd Idi ia)

(b) IO71V3 (d) 147t

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

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

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)

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

Khi cdt mat ndn bdi mot mat phdng

ta dupe hai dudng thang m va n m

Cdu hdi 2

m va n quan he nhu thi nao ?

Ggi y trd Idi cdu hdi 2

Hai dudng sinh m va n ddi xu:ng vdi

M ndm tren dudng trdn tam / ban kfnh

R = 01.tga va ndm trong (P) Vay mpiP) cdt mat ndn theo dudng trdn dd Ggi y trd Idi cdu hdi 3

Ne'u cdt mat ndn bdi mat phang

vuong gdc vdi true tai 0 thi ta dupe diem 0

• GV neu cac eau hdi:

H5 Mat ndn khac khd'i ndn d nhirng diem nao?

H6 Neu su khac nhau ciia dudng sinh mat ndn va hinh ndn

H7 Neu mdt sd hinh anh thuc t l vl hinh ndn

H8 Phai chang mat ndn cd gidi han bdi hai mat phdng song song vdi nhau

H9 Gdc giira dudng sinh va true ludn ludn khdng ddi

HIO Cd mdt phIp ddi xiing tam O biln mdi dilm cua mat ndn thanh mdi dilm ciia mat ndn

• GV md ta:

25

Cho tam gidc vudng lOM Khi quay nd xung quanh mdt cgnh gdc vudng

01 ta dugc mgt tgo thdnh mgt hinh dugc ggi Id hinh ndn trdn xoay Ta thudng ggi tat Id hinh ndn

• GV CO the dat cau hdi

H l l Hai tam giac lOM va lOM' cd bdng nhau khong?

H12 Hay neu tap hop dilm ciia M

• GV neu tilp khai niem:

O ggi Id dinh cua hinh ndn

IM ggi Id dudng sinh cua hinh ndn

10 ggi Id dudng cao cua hinh ndn

Tap hgp diem M Id dirdng iron tdm 1 bdn kinh IM ggi Id ddy ciia hinh ndn

Phdn hinh ndn bo di mat ddy ggi Id mat xung quanh ciia hinh ndn

HI3.10 vuong gdc vdi day Dung hay sai

H14 Gdc tao bdi dudng sinh va dudng cao bdng bao nhieu lan gdc d dinh

HI5 Hay neu khai niem dinh, day, dudng sinh, dudng cao ciia khdi ndn

• Thuc hien [T] trong 3'

Hoat dong eiia GV

Ggi y trd Idi cdu hdi 2

Cdt hlnh ndn bdi mat phdng di qua

true ta dupe mdt tam giac can OAB vdi day la dudng kfnh AB ciia dudng

trdn day

GV neu dinh nghia :

Hinh ndn cimg vdi phdn hen trong cua nd ggi Id kiwi ndn xdc dinh bdi hinh ndn dd

GV neu dinh nghia khac vl khdi ndn trdn xoay:

Khd'i ndn trdn xoay Id phdn khdng gian gidi hgn bai hinh ndn trdn xoay

vd cd hinh ndn

N Id diem trong ne'u N thudc khd'i ndn

N Id diem ngodi ne'u N khdng thudc khdi ndn

HOATDONC 3

3 Khai niem ve dien tich hinh ndn va the tich khdi ndn

HI6 Hay ve mot hinh chop cd tat ca cac dinh ciia day hinh chdp la da giac ndi tilp dudng trdn day Dinh triing vdi dinh ciia day

S

27

H17 Tam ciia da giac va tam ciia dudng trdn day luon triing nhau Diing hay sai?

• GV neu dinh nghia :

Dien lich xung quanh ciia hinh non 9)1 la gidi hgn ciia dien lich xung quanh ciia hinh chdp deu ndi tie'p 9)1 khi sd cgnh ddy tdng len vd hgn The lich ciia khdi ndn Ol Id gidi hgn ciia the tich ciia khdi chdp deu ndi tie'p Ol khi sd cgnh ddy tdng len vo hgn

H18 Dien tfch xung quanh ciia hinh chdp diu ndi tilp hinh ndn Idn hon hay nhd hon dien tfch xung quanh ciia hinh ndn?

HI9 Khi nao dien tfch hinh chdp va hinh ndn nhu tren triing nhau?

H20 Nhdc lai cong thiic tfnh dien tfch xung quanh eiia hinh chdp

• GV nhdc lai cong thiic : S^^^ = — PQ trong dd q la khoang each tir O den mot canh p la chu vi day

H21 Khi n ^•oo thi p dan den sd nao ?

• GV neu dinh If:

Dien lich xung quanh ciia hinh ndn bdng mdl nira chu vi ddy nhdn vdi do ddi dudng sinh

• GV neu tilp dinh nghia:

Tdng ciia dien lich xung quanh vd dien tich ddy ggi la dien lich todn phdn ciia hinh ndn

• GV neu dinh nghia :

The tich ciia hinh ndn trdn xoay la gidi hgn ciia the tich ciia hinh chdp deu ndi lie'p hinh ndn dd khi sd cgnh ddy idng len vd hgn

H22 Neu cdng thirc tinh the tfch hinh chdp

GV nhdc lai Vp = - B h

• 3

H23 Khi sd canh ciia hinh chdp dan tdi co thi dien tfch day dan den sd nao?

• GV neu cong thiic :

1 1 7 V„ = - B h = -7rr^h,

" 3 3

• Thuc hien vf du trong 5'

l \ v\

1- • A 1- ••.••.• - A

Hoat ddng ciia G v

Cdu hdi 1

Xac dinh ban kfnh day va dudng

sinh ciia hinh ndn

Cdu hdi 2

Tfnh dien tfch xung quanh, dien

tfch toan phan cua 9 l

Hoat ddng ciia HS

Ggi y trd Idi cdu hdi 1

Ban kfnh day la a va dp dai dudng sinh la 2a

Ggi y trd Idi cdu hdi 2

HS tu tfnh

29

HOATDONC 4

4 Thiet dien conic

• GV neu dinh nghia :

Ne'u cdt mat ndn trdn xoay bdi mgt mat phdng ( P ) khdng di qua dinh ciia mat ndn tin giao se Id :

Mgt dudng clip ne'u mp ( f ) cdt mgi dudng sinh (dgc biet, ne'u [P) vudng gdc vdi true mat ndn thi giao Id dudng iron)

- Mdt dudng hypebol ne'u mp [P) song song vdi hai dirdng sinh

Mdl dirdng parabol ne'u mp [P] song song vdi chi mdt dudng sinh

HOATDONC 5

TOM TflT Bfll HOC

1 Mat trdn xoay sinh bdi dudng thdng / khi quay quanh A gpi la mat ndn trdn xoay (hay vdn tdt la mat ndn)

A gpi la true ciia mat ndn

/ gpi la dudng sinh cua mat ndn

O gpi la dinh ciia mat ndn

Gdc 2(2 gpi la gdc d dinh ciia mat ndn

2 Phan ciia mat ndn 9)1 giai han bdi hai mat phdng (P) va (P') ciing vdi hinh trdn xac dinh bdi (v) dupe gpi la mdt hinh ndn

3 Hinh ndn ciing vdi phan ben trong ciia nd gpi la khdi ndn xac dinh bdi hinh ndn

do

4 Dien tfch xung quanh ciia hinh ndn bdng mot nira chu vi day nhan vdi dp dai

MOT SO CflU HOI TRflC NGHIEM

Hay diln diing (D) sai (S) vao cac khdng dinh sau :

Cdu 1

(a) Hinh ndn va hinh chdp la nhu nhau

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

(c) Hinh ndn la mot phan ciia mat ndn

(d) Ca ba khdng dinh tren diu sai

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

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

ta cd thi dupe mot hinh ndn

(c) Hinh ndn cd mot true ddi xung