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

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.. • GV ndu dinh nghla : Dien tich x

Chi/dNq 2

MAT NON, MAT T R U , MAT CAU

P h a n 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

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

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

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

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

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?

• 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:

• 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

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

• 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

5 Vi du

•GV cho HS tdm tit vf du:

Hoat ddng ciia GV

Cdu hdi 1

Tfnh chu vi niia dudng trdn ldn

Cdu hdi 2

So sanh chu vi ciia dudng trdn

day va niia chu vi dudng trdn ldn

Cdu hdi 3

Tfnh r

Hoat ddng cua HS

Ggi y trd ldi cdu hdi 1

Niia chu vi ciia dudng trdn ldn la chu

vi dudng trdn nhd va bing 27IT

Ggi y trd ldi cdu hdi 2

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

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:

• 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 :

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

B'

C

Hoat ddng cua GV

Cdu hdi 1

Tfnh ban kfnh ciia dudng trdn day

cua hinh tru

Hay chi ra va tfnh ban kfnh day

cua hinh tru

Hay chi ra va tfnh ban kfnh day

ciia hinh tru

Cdu hdi 2

Hay cbl ra va tfnh dudng cao ciia

hinh tru

Cdu hdi 3

Tinh thd tfch xung quanh

Ggi y trd ldi cdu hdi 2

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

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

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/

HOATDQNG 3

MQT SO CflU H6r TR^C NGHl|M

Hay didn diing (D) sai (S) vao cac khang 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 mdt phin ciia mat ndn

(d) Ca ba khang dinh trdn ddu sai

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

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

ta cd the duge mdt hinh ndn

(e) Hinh ndn cd mdt true ddi xumg

(d) Ca ba khang dinh trdn ddu sai

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

(a) Mat tru trdn xoay khi gidi han bdi hai mat phang

song song ta dugc hinh tru

(b) Mat tru trdn xoay khi gidi han bdi hai mat phing

vudng gdc vdi true ta dugc hinh tru

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

(d) Ca ba khang dinh trdn ddu sai

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

Didn tfch xuhg quanh ciia hinh chdp la :

Dudng sinh la:

Didn tfch toan phin ciia hinh ndn la:

Cdu 15 Cho hinh lang tru luc giac ddu canh day la 2V3 ndi tie'p mdt hinh tru cd

Dien tich xung quanh cua hinh tru la

Thd tfch ciia hinh tru la :

Hoat ddng cua GV

Cdu hdi 1

Ggi O la tam dudng trdn, A la

dudng thing di qua tam 0 va A ±

(P) m la dudng thing bat ki ai

qua mdt diem thugc dudng trdn

Tim mdi quan he cua m va A

m each A mgt khoang khdng ddi

Ggi y trd ldi cdu hdi 2

Dua vao dinh nghla

Ggi y trd ldi cdu hdi 3

Bai 3 Hudng ddn Dua vao tinh chat cua da didn va hinh lap phuang

Hinh lap phuang cd 8 dinh va 6 mat

Sd canh cua hinh lap phuang la 6

Ggi y trd ldi cdu hdi 3

Tam giac SOA la tam giac vudng tai

O Tir dd ta cd dudng sinh

Tif dd ta cd IO = 15em

Ggi y trd ldi cdu hdi 3

Dua vao tam giac vudng SOI ta cd

Ggi y trd ldi cdu hdi 2

S^q=2Tirl = 2Ti.5.7 = 707i

Ggi y trd ldi cdu hdi 3

V - 7 i r 2 h = 71.5^7 = 17571

caub

Ggi y trd ldi cdu hdi 3

Dudng cao eiia hinh tru la :

SO= aV3

Ggi y trd ldi cdu hdi 4

1 2 S„„ = — 27ta.2a = 2Tia xq 2

Cdu hdi 5

Tfnh thd tfch cua hinh tru

Ggi y trd ldi cdu hdi 5

na' N-—na h = —Tta av3

3 3 3

^

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

xung quanh va the tfch hinh tru

Ke AA' // OO' xac dinh mdl

quan he giira 0 0 ' va mp(AA'B)

Ggi y trd ldi cdu hdi 3

La khoang each giiia 0 0 ' va

mp(AA'B) Ke O'H 1 A'B OH ehfnh

hinh tru va hinh ndn

A O"

/ / / /

/.y—[-r / do

M

Dd tfnh didn tfch xung quanh ciia

hinh ndn ta cin tfnh gi

= 2r

caub

Hoat ddng ciia GV

Cdu hdi 1

Thd tfch khdi ndn bing bao nhidu

phin thd tfch khdi tru

Cdu hdi 2

Thd tfch phin cdn lai bing bao

nhidu thd tfch khdi tru

Bai 9 Hudng ddn Dufa vao dinh nghla, tfnh cha't, dien tfch xung quanh va the tfch

hinh tru va hinh ndn

cau a

Hoat ddng ciia GV

Cdu hdi I

Gia sii khi cit hinh ndn ta dugc

tam giac SAB Xac dinh gdc

vudng va dd dai cae canh

xq 2 2

Bai 10 Hudng ddn Dua vao dinh nghla, tfnh chat, dien tfch xung quanh va thd tfch

hinh tru va hinh ndn

D

A ' « 1

-^^ma

Ggi y trd ldi cdu hdi I

Hinh chii nhat

Ggi y trd ldi cdu hdi 2

A C = 2r

Ggi y trd ldi cdu hdi 3

Tacd BC'^ = AC^ - AB^ - 4r2 - AB^

MOT SO CAU HOI ON TAP HOC Kl 1

(d) Ca ba cau trdn ddu sai

B' C

(a) Thd tfch hinh hop la abc

(b) Thd tfch hinh chdp A'.ABCD la abc

(c) The tfch hinh chdp A'.ABCD la - abc

(a) Thd tfch hinh hop la abc

(b) Thd tfch hinh chdp A'.ABD la abc

D

D

D

(c) Didn tfch tam giac SBD bing

(d) Ca ba cau trdn ddu sai

Cdu 5 Cho hinh lap phuang ABCDA'B'CD' canh a

/ \

A' 1 / B

/ /

/

r

D'

(a) Thd tfch khdi lap phuang la a'

(b) Thd tich khdi chdp A'.ABCD la -a^

(c) Thd tich khdi lang tru ABDA'B'D' la -a^

6 (d) Ca ba cau tren ddu sai

Chgn cdu trd ldi ddng trong cdc bdi tap sau:

Cdu 6 Cho hinh chdp SABCD, day ABCD la hinh thang vudng tai A,

SA l(ABCD), SA = a, AB = 2a, AD = DC = a Khoang each tur B de'n (SAD) la

(a) a ; (b) 2a

(c) ayfs ; (d)aV2

Trd ldi (b)

Cdu 7 Cho hinh chdp SABCD, day ABCD la hinh thang vudng tai A,

SA J.(ABCD), SA = a, AB = 2a, AD = DC = a Thd tfch khdi chdp la

(c) (d) Ca ba cau trdn ddu sai

Trd ldi (a)

Cdu 8 Cho hinh chdp SABCD, day ABCD la hinh thang vudng tai A,

SA ±(ABCD), SA = a, AB = 2a, AD = DC = a The tfch khdi chdp S.ABC la

(a)

-f (d) Ca ba cau trdn ddu sai

Trd ldi (b)

Cdu 9 Cho hinh chdp SABCD, day ABCD la hinh thang vudng tai A,

SA ±(ABCD), SA = a, AB = 2a, AD = DC = a Khoang each giiia SA va BC la: