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

Muc dich ciia chuong • Chuang II nham cung ca'p cho hpc sinh nhiing kien thdc co ban ve khai niem cac khd'i trdn xoay trong khdng gian ma chii yeu la mat ndn, mat tru va mat cau.. • GV n

T R A N VINH

I hiet ke bai giang

H)NHHQC|2

TAP HAI

Chi/dNq 2

M A T NON, M A T T R U , M A T C A U

P h a n 1

Gidl THlfu CHL/CJNG

I CAU TAG CHUONG

§ 1 Khai niem ve mat trdn xoay

§ 2 Mat eau

On tap chuang II

I Muc dich ciia chuong

• Chuang II nham cung ca'p cho hpc sinh nhiing kien thdc co ban ve khai niem cac khd'i trdn xoay trong khdng gian ma chii yeu la mat ndn, mat tru va mat cau Mat ndn trdn xoay : Day, dudng sinh va dudng trdn day

Dien tich xung quanh va dien tich toan phan ciia mat ndn

The tfch ciia mat ndn

• Mat tru trdn xoay la gi ?

Dien tich xung quanh va dien tich toan phSn cua mat tru

The tfch ciia mat tru

• Mat eSu la gi ?

Dien tfch ciia mat cau

Thi tich ciia mat cau

II M U C TIEU

1 Kien thiirc

Nam dupe toan bp kien thiic ca ban trong chuong da neu tren

Hieu cac khai niem cac mat trdn xoay: Mat ndn, mat tru va mat eau

Nam dupe eac cdng thiic tfnh dien tfch, the tfch cua eac mat trdn xoay

Ket ludn:

Khi hpc xong chuong nay hpc sinh can lam tdt eac bai tap trong sach giao khoa va lam dupe cac bai kiem tra trong chuong

1 Khai niem chung vd mat cau

2 Diem thudc mat cau , diem d trong va diem d ngoai mat cSu

3 Giao cua mat cau va mat phang

4 Giao cua mat cdu va dudng thang

5 Tie'p tuye'n ciia mat cau

6 The tfch va dien tich cua mat c^u

2 KI nang

• Ve thanh thao cac mat cau

• Xac dinh dupe mdt mat phang la tie'p dien cua mat cau, mot mat phang la tie'p tuye'n cua mat cau

• Xac dinh dupe vi trf tuong ddi cua mat phang va mat eau

• Tfnh dupe the tfch va dien tfch cua mat cau

3 Thai do

• Lien he dupe vdi nhieu van de thuc te' trong khdng gian

• Cd nhieu sang tao trong hinh hpc

• Hiing thii trong hpc tap, tfch cue phat huy tfnh dpc lap trong hpc tap

II CHUAN BI CUA GV VA HS

1 Chuan bi ciia GV:

• Hinh ve 2.15 de'n 2.26

• Thudc ke, phan mau,

2 Chuan bi cua HS :

Dpc bai trudc d nha, cd the lien he cac phep bien hinh da hpc d Idp dudi

in DHAN PHOI TH6I LUONG

Bai dupe chia thanh 5 tiet:

Tie't 1: Tir dau den het phan I

Tie't 2: Tie'p theo de'n het phan II

Tie't 3: Tie'p theo den het phan III

Tie't 4: Tie'p theo den het phan IV

Tie't 5: Hudng din bai tap

IV TIEN TDlNH DAY HOC

R. Bni 1V161

HOATDONCl

I MAT CAU VA KHAI NIEM L I £ N QUAN DEN MAT CAU

1. Mat cau

GV neu cau hdi :

HI Em hay neu khai niem hinh cau theo each nghi ciia minh

H2 Qua dia ciu cd phai la hinh ciu hay khdng?

• GV su dung hinh 2.14 trong SGK va dat van de:

H3 Cho hai diem M^ va M2, hay so sanh OM^ va OMj

H4 Khi cat mdt mat eau va mdt dudng thing di qua O, ta dupe nhiing doan thang Hay so sanh cac doan thang dd

H5 Mdt doan thang di qua O eat mat cau tai A va B Hay neu vi trf ciia O ddi vdi

A v a B

H6 Mdt doan thang di qua O cat mat cau tai A va B Mdt diem M bat ki tren mat

cau dd Hay do gdc AMB

H7 Neu dinh nghia mat cau theo y ciia em

• GV neu dinh nghia :

Tap hgp nhirng diem cdch deu mgt diem O cho trUdc mgt khodng khdng ddi la mgt mat cdu

H8 Hay neu kf hieu dudng trdn tam O ban kfnh R

H9 Day cung cua dudng trdn la gi ?

HIO Hay ndu tfnh chat ciia day cung Idn nhat

• GV neu dinh nghia dudng kfnh cua dudng trdn:

Dudng kinh cua dudng trdn la ddy cung di qua O

H I 1 Hay so sanh dp dai eiia dudng kfnh vdi ban kfnh, vdi day cung bat ki?

H12 Khi bie't dudng kfnh ciia mat cau thi cd xac dinh dupe tam va ban kinh cua mat cau hay khdng?

• GV neu su xac dinh cua mat cau:

Mgt mat cdu xdc dinh khi bie't tdm vd bdn kinh hoac dudng kinh ciia nd

2 Diem nam trong va nam ngoai mat cau Khd'i cau

HI3 M thudc mat cau (O ; R) Hay so sanh OM va R

H14 M d ben trong mat cau (O ; R) Hay so sanh OM va R

H15 M d ben ngoai mat cau (O ; R) Hay so sanh OM va R

• GV neu cac khai niem diem nam trong, nam tren va nam ngoai mat cau va cho

HS dien vao bang sau:

• GV neu dinh nghia khd'i eau

Tap hgp tdt cd cdc diem thudc mat cdu S(0; R) vd tdt cd cdc diem d trong mat cdu ggi la khdi cdu

HI6 Danh dau x vao 6 ma M thuoc khd'i cau

3 Bieu di^n mat cau

• GV neu eac bieu dien khd'i cau theo y sau

Ve mdt dudng trdn

Tam mat cau la tam dudng trdn

- Cac mat phang cdn lai cat mat cau la mdt hinh dupe bieu dien la hinh Elip

Tham khao hinh 2.16

• GV neu qua ve each bieu dien mat cau nhd phep chie'u

HI7 Hay ve mdt mat cau di qua ba diem A, B va C Mat cau dd cd duy nhat khdng?

4 Dudng kinh tuye'n va vl tuye'n cua mat cau

HIS Hay neu khai niem dudng kinh tuye'n va vT tuye'n trong dia If

• GV sii dung hinh 2.17 va dat cac cau hdi:

HI9 Kinh tuyen la ca dudng trdn Idn hay niia dudng trdn Idn?

H20 Hay ve kinh tuye'n va vi tuye'n

• GV neu dinh nghia kinh tuye'n va vl tuye'n:

Giao CIM mat cdu vd nira mat phdng cd bd la true cua mat cdu ggi la kinh tuye'n Giao ciia mat cdu vd mat phdng vudng gdc vdi true ciia nd ggi la vT tuye'n

• Thuc hien ^ 1 trong 4 phiit

Ggi y trd Idi cdu hdi 1

Tam giac can

Ggi y trd Idi cdu hdi 2

Gpi H la trung diem AB ; OH cd

dac diem gi ?

Cdu hoi 3

0 thudc mat phang nao ?

OH 1 AB

Goi y trd Idi cdu hoi 3

Mat phang trung true ciia AB

HOATDONC 2

II GIAO CUA MAT CAU VA MAT PHANG

GV sii dung hinh 2.18

Dat OH = h ;

1 Trudng hpp h > r

H 2 1 S o s a n h O M v a r

H22 M nam trong hay ngoai mat cau?

• GV ket luan M nam ngoai mat ciu va giao ciia mat ciu va mat phang la khdng cd

2 Trudng hpfp h = r

H23 H thuoc S Diing hay sai ?

H24 M 7^ H thi M khdng thudc S Diing hay sai

• GV ket luan :

Giao cua mat cau S va mat phang P: Mat phang (P) tiep xiic vdi mat cau

• Dua vao hinh 2.19 GV dua ra cac cau hdi sau:

H25 Mpi dudng thing thudc (O) khong di qua H cd giao vdi mat ciu hay khdng?

• GV neu dinh If:

Dieu kien cdn vd du de mat phang (P) tie'p xuc vdi mat cdu S(0 ; r) tgi H

la (P) vudng gdc vdi bdn kinh OH tgi H

H26 Mpi mat phing vudng gdc vdi OH deu tiep xiic vdi S Diing hay sai ?

H27 Chiing minh khi (P) tie'p xiic vdi S tai H thi OH < OM

2 Trudng hop h < r

Trong hinh 2.20

H28 H thudc mien trong cua S Diing hay sai ?

H29 M thudc (P), M thuoc S thi OM cd dac diem gi ?

H30 Cho OH = h tfnh HM

• GV ket luan :

Giao cua mat ciu S va mat phang P la dudng trdn tam H ban kfnh r' - yr -h

H31 Khi h = 0, tim tam dudng trdn la giao cua (P) va (S)

• GV neu ket luan

Mat phdng di qua tdm ggi la mat phdng kinh Giao ciia (P) vd (S) Id dudng trdn vd ggi la dudng trdn Idn

• Thuc hien A2 trong 5'

HOATDONC3

MAT CAU

1 Dinh nghia

• GV su dung hinh 2.22 va dat ra cac cau hdi:

GV cho HS chi ra doan thing d, r

1 Trudng hop d > r

H32 So sanh OM va OH

H33 M d trong hay ngoai mat cau?

H34 A cd cat mat cau hay khdng?

• GV neu dinh nghia:

Khi d > r thi A vd (S) khdng cdt nhau

2 Trudng hgp d = r

• GV sii dung hinh 2.23 va dat ra eac cau hdi:

H 3 5 S o s a n h O M v a O H

H33 M ?^ H thi M d trong hay ngoai mat cau?

H34 A cd cat mat cau hay khdng?

• GV neu dinh nghia:

Khi d = r thi A vd (S) tie'p xuc nhau

• GV neu dinh If:

Dieu kien cdn vd du de A tie'p xdc vdi mat cdu S(0 ; r) tgi H la A vudng gdc vdi bdn kinh OH tgi H

Khi d < r thi dudng thdng A cdt (S) tgi hai diem phdn biet

• GV dat bai toan : Cho biet d, r hay tfnh MN

• De tdng ket GV nen cho HS dien bang sau :

• GV tdng ket chii y bdi bang sau :

Qua mdt diem d tren

TJNH CHAT CUA CAC TIEP TUYEN

Cac tiep tuyen cimg vudng gdc vdi ban kfnh tai tiep diem

Dp dai eac doan thing ndi diem

dd va tiep diem bang nhau

Gpi O la tam ciia hinh vudng

canh a Chiing minh 0 la giao

diem cua cac dudng cheo

Hoat ddng ciia HS

Gffi y trd Idi cdu hoi 1

HS tu chiing minh

Gpi 0 la tam cua hinh vudng

canh a Chiing minh 0 la giao

diem ciia cac dudng cheo

Gpi O la tam cua hinh vudng

canh a Chiing minh O la giao

diem cua cac dudng cheo

HOATDONC 4

IV CONG THtrC DI$N TICH MAT CAU VA T H ^ TICH MAT CAU

• GV neu cdng thuc dien tfch mat cau:

Thuc hien ^ 4 trong 5'

Hoat ddng cua GV

Cdu hdi 1

Xac dinh tam va ban kfnh mat

cau ngoai tiep hinh lap phuong

Cdu hdi 2

Tfnh the tfch V

Hoat ddng cua HS

Gffi y trd Idi cdu hdi 1

Tam O la tam hinh lap phuong, ban

2 Mgt mat cdu xdc dinh khi bie't tdm vd bdn kinh hoac dudng kinh cda nd

3 Tap hgp tdt cd cdc diem thudc mat cdu S(0; R) vd tdt cd cdc diem a trong mat cdu ggi Id khdi cdu

4 Dieu kien cdn vd du de mat phdng (P) tie'p xdc vdi mat cdu S(0 ; r) tgi H Id (P) vudng gdc vdi bdn kinh OH tgi H

5 Mat phdng di qua tdm ggi la mat phdng kinh Giao ciia (P) vd (S) la dudng trdn

vd ggi la dudng trdn Idn

Giao cua Ava (S)

d > r Khdng cd

MQT SO Cfia HOI T R 6 C NGHIEM

Hay dien dung (D) sai (S) vao cac kh^ng djnh sau :

Cdu 1

(a) Mdt mat phing cit hinh cSu thi cat theo mdt dudng trdn

(b) Dudng trdn Idn ed ban kfnh bang ban kfnh mat ciu

(c) Dudng trdn Idn di qua tam O

(d) Mdt hinh ciu cd vd sd dudng trdn Idn

(a) Mdt dudng trdn xoay quanh mdt dudng thing ta dupe mdt liinh cdu [ ]

(b) Mdt mat ciu quay quanh mdt dudng kfnh cua nd ta dupe mdt mat eSu [ ]

(c) Niia dudng trdn quay quanh mdt dudng kinh ciia nd ta dupe mdt mat ciu [ ]

(d) Ca ba khang dinh tren deu sai [1

Cdu 3 Gpi d la khoang each tii O cua mat cau S(0 : r) den mat phing (P)

(a) d > r thi (P) cat (S) D (b) d < r thi (P) cit (S) [ ] (c) d = r thi (P) cit (S) D (d) Ca ba khang dinh tren deu sai U

Cdu 4 Gpi d la khoang each tii O ciia mat cau S(0 ; r) den mat phang (P)

(a) d > r thi (P) tiep xiic vdi (S) •

(b) d < r thi (P) tiep xiic vdi (S) [ ]

(c) d = r thi (P) tie'p xiic vdi t (S) [ ]

(d) Ca ba khing dinh tren deu sai |_|

Chon khang dinh dung trong cac cau sau:

Cdu 5 Gpi d la khoang each tilt O cua mat ciu S(0 ; r) de'n mat phing (P)

Dien vao chd trdng sau :

Cdu 6 Gpi d la khoang each tir O ciia mat cau S(0 ; r) den dudng thing A

Dien vao chd trdng sau :

Cdu 7 Cho hinh lap phuang ABCD A'B'C'D' tam O Tam cua mat cau ngoai tiep

hinh lap phuong la:

(a) O; (b) A;

(c) B; (d) C

Trd Idi (a)

Cdu 8 Cho hmh lap phuong ABCD A'B'C'D' tam O Tam ciia mat ciu tiep xiic

vdi tat ca cac mat ciia hinh vudng hinh lap phuong la :

(a) O; (b) A;

(c) B; (d) C

Trd Idi (a)

Cdu 9 Cho hinh lap phuong ABCD A'B'C'D' canh a Ban kfnh cua mat cau tiep

xiic vdi tat ca cac mat cua hinh lap phuong la :

Cdu 10 Cho hinh lap phuong ABCD A'B'C'D' canh a Ban kfnh cua mat cau

ngoai tie'p hinh lap phuong la :

Cdu 11 Cho hinh lap phuong ABCD A'B'C'D' canh a Dien tfch xung quanh ciia

mat cau tie'p xiic vdi tat ca cac mat ciia hinh vudng hinh lap phuong la :

(a) 47ta"; (b)7ia^

(c) 87ra^; (d) 127ia^

Trdldi (b)

Cdu 12 Cho hinh lap phuang ABCD A'B'C'D' tam O The tfch ciia mat cau tiep

xiic vdi tat ca cac mat cua hinh vudng hinh lap phuong la :

Cdu 13 Cho hinh chdp S.ABC ndi tie'p hinh ciu tam O ban kinh r (hinh ve)

Biet tam giac ABC la tam giac deu, SO 1 (ABC) Canh AB bing

(a)rV3; (b)2rV3 (c)4rV3; (d)3rV3

Trd Idi (a)

Cdu 14 Cho hinh chdp S.ABC ndi tiep hinh cau tam O ban kfnh r (hinh ve)

Cdu 16 Cho hinh cau S(0 ; 4) nhu hinh ve

Ban kfnh dudng trdn tam O bing :

(a) V7;

( c ) 3 ;

Trdldi (a)

(b)3V7 (d)6

HOATDQNC 7

naOTNG D^N Bfil TOP SGK

Bai 1 Hudng ddn Sii dung dinh nghia hinh eau:

Ddp sd Mat ciu tam O (trung diem AB) ban kinh AB

Bai 2 Hudng ddn Dua vao tfnh chat cua mat phang tmng true va dinh nghia mat eau:

Bai 3 Hudng ddn Dura vao tfnh chit ciia giao diem mat cau va mat phang

Tap hop la dudng thing di qua tam O' cua dudng trdn va A 1 mp(O')

Bai 4 Hudng ddn Dua vao dinh nghia mat cau

A

Goih (O') la dudng trdn ndi tiep tam giac ABC Sii dung bai 3

Bai 5 Hudng ddn Dua vao vf trf tuong ddi cua mat phang va mat cau:

Bai 6 Hudng ddn Dua vao tfnh chat tie'p tuyd'n ciia mat ciu

- Chiing minh Al va BI la hai tie'p tuyen cua mat ciu

- Chiing minh AMAB = ALAB

Bai 7 Hudng ddn Dua vao dinh nghia hinh tru, tfnh chat ciia hinh tru, dien tfch

xung quanh va the tfch hinh tru

Bai 9 Hudng ddn HS tu giai

Bai 10 Hudng ddn HS tu giai

On tap churdng II (tiet 11,12)

1 MUC TIEU

1 Kien thurc

HS n i m duac:

1 Khai niem chung ve mat trdn xoay

2 Mat tru va cac tfnh chat ciia mat tru

3 Mat cau va cac tfnh chat cua mat cau

4 Giao ciia mat cau va dudng thing

5 Tiep tuyen ciia mat cau

6 The tfch va dien tfch ciia mat cSu

2 KI nang

• Giai thanh thao cac bai toan lien quan den mat ciu, mat tru

• Xac dinh dupe mdt mat phing la tie'p dien cua mat ciu, mdt mat phing la tie'p tuyen ciia mat cau

3 Thai dp

• Lien he dupe vdi nhieu vin de thuc te' trong khdng gian

• Cd nhieu sang tao trong hinh hpc

• Hiing thii trong hpc tap, tfch cue phat huy tfnh dpc lap trong hpc tap

II CHUAN DI CUA GV VA HS

ra PHAN PHOI THOI LUONG

Bai dupe chia thanh 2 tie't :

Tie't 1: Chiia bai tap va on tap

Tie't 2: Kiem tra 1 tie't

IV TIEN TDINH DAY HOC

HOATDONC 1

I. M O T s d CAU HOI ON TAP

Cdu hdi 1 Neu dinh nghia mat trdn xoay

Cdu hdi 2 Neu mdt sd hinh trdn xoay trong thuc te ma em biet

Cdu hdi 3 Mdt tam giac thudng quay quanh mdt canh cd dupe mdt hinh ndn khdng? Cdu hdi 4 Mdt hinh ndn dupe tao thanh nhu the nao?

Cdu hdi 5 Mdt hinh binh hanh quay quanh mdt canh cd dupe mot hinh tru khdng? Cdu hdi 6 Mdt hinh tru dupe tao thanh nhu the' nao?

Cdu hdi 7 Neu khai niem true, dudng sinh va dudng cao cua hinh ndn

Cdu hdi 8 Day ciia hinh ndn la hinh gi?

Cdu hdi 9 Neu khai niem true, dudng sinh va dudng cao cua hinh tru

Cdu hdi 10 Neu dinh nghia mat ciu bing cac each khac nhau

Cdu hdi 11 Hinh cau va mat ciu khac nhau nhu the' nao?

Cdu hdi 12 TCr mdt diem ke hai tie'p tuyen de'n mat cau

a) Khi nao thi ke dupe?

b) Neu cac tfnh chat cua hai tiep tuyen dd

Cdu hdi 13 Neu cac vi trf tuong ddi ciia mat phing va mat cau

Cdu hdi 14 Neu cac vi trf tuong ddi eiia dudng thing va mat ciu

Cdu hdi 15 Neu sU xac dinh mat cau

Cdu hdi 16 Neu cac cdng thiic tinh dien tfch mat ciu va the tfch khd'i ciu

HOATDONC 2

n MOT s o CAU HOI TRAC NGHIEM ON TAP CHUONG II

Hay chon cau tra Idi dung

Cdu 1 Cho hinh chdp ndi tiep mdt hinh ndn

(a) Hai hinh chdp va hinh ndn cd dudng cao trdng nhau;

(b) The tfch hinh chdp va the tfch hinh ndn bing nhau;

(c) The tfch hinh chdp Idn hon the tfch hinh ndn;

(d) Ca ba y tren deu diing

Trd Idi (a)

Cdu 2 Cho hinh chdp luc giac ddu canh day la 2V3 ndi tiep mdt hinh ndn cd

dudng cao la 3

S

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

Cdu 5 Cho hinh lang tru luc giac deu canh day la 2\/3 ndi tiep mdt hinh tru cd

Dudng sinh ciia hinh tru la :

(a)2V3;

( c ) 3 ;

Trd Idi (c)

(b)3V3 (d)6

Cdu 7 Mdt hinh ciu cd dudng trdn Idn ngoai tiep mdt tam giac deu canh 1 cd ban

Cdu 9 Gpi d la khoang each til O ciia mat ciu S(0 ; r) den mat phing (P)

Dien vao chd trdng sau :

Cdu 10 Gpi d la khoang each tii O ciia mat cau S(0 ; r) den dudng thing A

Dien vao chd trdng sau :

Cdu II Cho hinh lap phuong ABCD A'B'C'D' tam O Tam ciia mat cau ngoai

tie'p hinh lap phuong la

(a) O; (b) A

(c) B; (d) C

Trd Idi (a)

Cdu 12 Cho hinh lap phuang ABCD A'B'C'D' tam O Tam ciia mat ciu tiep xuc

vdi tat ca cac mat cua hinh vudng hinh lap phuong la :

(a) O; (b) A

(c) B; (d) C

Trd Idi (a)