TRAN VINH I hiet ke bai giang H)NHHQC|2 TAP HAI N H A X U A T B A N H A N0I TRAN VINH THIET KE BAI GIANG H I N H HOC 12 TAP NHA XUAT B A N HA NOI Chi/dNq M A T NON, M A T T R U , M A T C A U Phan Gidl THlfu CHL/CJNG I CAU TAG CHUONG § Khai niem ve mat trdn xoay § 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 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 Kien thiirc Nam dupe toan bp kien thiic ca ban 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 KI nang Tinh dupe dien tfch xung quanh, dien tfch toan phan ciia cac hinh trdn xoay Tfnh dupe the tfch cua hinh lang tru, hinh ndn Thai Hpc xong chuong hpc sinh se lien he dupe vdi nhieu van de thuc te sinh ddng, lien he dupe vdi nhiing van de hinh hpc da hpc d Idp dudi, md mdt each nhin mdi ve hinh hpc Tii dd, cac em cd the tu minh sang tao nhiing bai toan hoac nhiing dang toan mdi Ket ludn: Khi hpc xong chuong hpc sinh can lam tdt eac bai tap sach giao khoa va lam dupe cac bai kiem tra chuong Phan cAc &Al SOAN {Ti^p theo) §2 Mat cau (tiet 6, 7, 8, 9, 10) I MUC TIEU Kien thurc HS nam duoc: Khai niem chung vd mat cau Diem thudc mat cau , diem d va diem d ngoai mat cSu Giao cua mat cau va mat phang Giao cua mat cdu va dudng thang Tie'p tuye'n ciia mat cau The tfch va dien tich cua mat c^u KI nang • Ve 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 Thai • Lien he dupe vdi nhieu van de thuc te' khdng gian • Cd nhieu sang tao hinh hpc • Hiing thii hpc tap, tfch cue phat huy tfnh dpc lap hpc tap II CHUAN BI CUA GV VA HS Chuan bi ciia GV: • Hinh ve 2.15 de'n 2.26 • Thudc ke, phan mau, 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 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 n DAT VAN D€ Cau hdi Hinh trdn xoay la gi ? Hay ke mdt vai hinh trdn xoay da hpc Cau hdi Hau ndu each tao hinh ndn va hinh tru C^u hdi Mat tru trdn xoay va hinh tru gidng va khac d nhihig diem nao? R Bni 1V161 HOATDONCl I MAT CAU VA KHAI NIEM L I £ N QUAN DEN MAT CAU 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 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 AvaB H6 Mdt doan thang di qua O cat mat cau tai A va B Mdt diem M bat ki tren mat cau dd Hay 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 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 bie't tdm vd bdn kinh hoac dudng kinh ciia nd Diem nam 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 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: OM R Tren Vi trf • 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 mat cdu ggi la khdi cdu HI6 Danh dau x vao ma M thuoc khd'i cau OM 3 R Thudc khd'i cau 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 nhat khdng? Dudng kinh tuye'n va vl tuye'n cua mat cau HIS Hay neu khai niem dudng kinh tuye'n va vT tuye'n 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 ^ phiit Hoat ddng cua GV Cdu hdi Tam giac ABC cd dac diem gi? Cdu hdi Hoat ddng ciia HS Ggi y trd Idi cdu hdi Tam giac can Ggi y trd Idi cdu hdi Gpi H la trung diem AB ; OH cd OH AB dac diem gi ? Goi y trd Idi cdu hoi Cdu hoi Mat phang trung true ciia AB thudc mat phang nao ? HOATDONC II GIAO CUA MAT CAU VA MAT PHANG GV sii dung hinh 2.18 Dat OH = h ; Trudng hpp h > r H21.SosanhOMvar H22 M nam hay ngoai mat cau? • GV ket luan M nam ngoai mat ciu va giao ciia mat ciu va mat phang la khdng cd 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 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 (P) tie'p xiic vdi S tai H thi OH < OM 10 Bai Hudng ddn Dua vao dinh nghia mat cau A Goih (O') la dudng trdn ndi tiep tam giac ABC Sii dung bai Bai Hudng ddn Dua vao vf trf tuong ddi cua mat phang va mat cau: cau a Chiing minh diem A, B, C va D ciing thudc mdt dudng trdn cau b Hudng ddn Ta cd MA MB = MO'^ - r'l Trong dd r' la ban kfnh dudng trdn tam O' MO'2 = MO^ - 0 ' ^ = d^ - 0 ' r'2=r^-00'2 26 Bai 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 Hudng ddn Dua vao dinh nghia hinh tru, tfnh chat ciia hinh tru, dien tfch xung quanh va the tfch hinh tru B \ O cau a Chiing minh O la giao diem eac dudng cheo la tam ciia mat ciu ^ a^+b^+c^ cau b Tam O' la tam hmh chu nhat ABCD Va 2+b2 Bai Hudng ddn Dua vao tfnh chat ciia tie'p tuye'n mat ciu HS tu giai Bai Hudng ddn HS tu giai Bai 10 Hudng ddn HS tu giai 27 On tap churdng II (tiet 11,12) MUC TIEU Kien thurc HS n i m duac: Khai niem chung ve mat trdn xoay Mat tru va cac tfnh chat ciia mat tru Mat cau va cac tfnh chat cua mat cau Giao ciia mat cau va dudng thing Tiep tuyen ciia mat cau The tfch va dien tfch ciia mat cSu KI nang • Giai 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 Thai dp • Lien he dupe vdi nhieu vin de thuc te' khdng gian • Cd nhieu sang tao hinh hpc • Hiing thii hpc tap, tfch cue phat huy tfnh dpc lap hpc tap II CHUAN DI CUA GV VA HS C h u a n bi cua G V : • Thudc ke, phan mau, Chuan bj cua HS : Dpc bai trudc d nha, cd the lien he cac phep bie'n hinh da hpc d Idp dudi 28 PHAN PHOI THOI LUONG Bai dupe chia tie't : Tie't 1: Chiia bai tap va on tap Tie't 2: Kiem tra tie't IV TIEN TDINH DAY HOC HOATDONC I M O T s d CAU HOI ON TAP Cdu hdi Neu dinh nghia mat trdn xoay Cdu hdi Neu mdt sd hinh trdn xoay thuc te ma em biet Cdu hdi Mdt tam giac thudng quay quanh mdt canh cd dupe mdt hinh ndn khdng? Cdu hdi Mdt hinh ndn dupe tao nhu the nao? Cdu hdi Mdt hinh binh hanh quay quanh mdt canh cd dupe mot hinh tru khdng? Cdu hdi Mdt hinh tru dupe tao nhu the' nao? Cdu hdi Neu khai niem true, dudng sinh va dudng cao cua hinh ndn Cdu hdi Day ciia hinh ndn la hinh gi? Cdu hdi Neu khai niem true, dudng sinh va dudng cao cua hinh tru Cdu hdi 10 Neu dinh nghia mat ciu bing cac each khac Cdu hdi 11 Hinh cau va mat ciu khac 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 29 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 n MOT s o CAU HOI TRAC NGHIEM ON TAP CHUONG II Hay chon cau tra Idi dung Cdu 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 Cho hinh chdp luc giac ddu canh day la 2V3 ndi tiep mdt hinh ndn cd dudng cao la S 30 Dudng cao ke tii S ciia mdi mat bdn ciia hinh chdp la : (a)2VlO; (c) (b)VlO To (d)10 Trdldi (b) Cdu Cho hinh chdp luc giac deu canh day la 2v3 ndi tiep mdt hinh ndn cd dudng cao la s Ban kfnh dudng trdn day la (a) 2V3; , , 2V3 (b) 2V6 (d) V3 Trd Idi (a) Cdu Cho hinh chdp luc giac deu canh day la 2v3 ndi tiep mdt hinh ndn cd dudng cao la S Dudng sinh la (a) ^ ; (b) 2V6 , , 2V3 (0—, (d) V3 Trdldi (b) 31 Cdu Cho hinh lang tru luc giac deu canh day la 2\/3 ndi tiep mdt hinh tru cd dudng cao la B C "^ B' A' , ^- Dien tfch xung quanh cua hinh lang tru la la : (a)36V3; (b) 16V3 (c)46V3; (d)26V3 Trd Idi (a) Cdu Cho hinh lang tru luc giac deu canh day la 2V3 ndi tiep mot hinh tru cd dudng cao la A B B' A' D' E' 32 Dudng sinh ciia hinh tru la : (a)2V3; (b)3V3 (c)3; (d)6 Trd Idi (c) Cdu Mdt hinh ciu cd dudng trdn Idn ngoai tiep mdt tam giac deu canh cd ban kfnh la (a) 27i; (b)37t (d)6 Trd Idi (e) Cdu Mdt hinh cau cd dudng trdn Idn ngoai tiep mdt tam giac deu canh cd dien tfch toan phan la : H hoc 12/2 33 (a)2V3; (b)3V3 (c)-i=; V3 (d) 671 Trd Idi (c) Cdu Gpi d la khoang each til O ciia mat ciu S(0 ; r) den mat phing (P) Dien vao chd trdng sau : d r 4 Vi tri tuang ddi cda (P) vd (S) Cdu 10 Gpi d la khoang each tii O ciia mat cau S(0 ; r) den dudng thing A Dien vao chd trdng sau : d 4 r 5 Vi tri tuang ddi ciia A vd (S) 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) 34 HOATDONC m HUONG DAN BAI TAP SGK Bai Hudng ddn cau a diing vi : Qua ba diem ABC ta cd mdt mat phing Giao ciia mat ciu va mat phing la dudng trdn Bai Hudng ddn D Dudng sinh ciia hinh ndn : BD - av2 Dudng cao ciia hinh ndn AB = a 35 Bai Hudng ddn Til tam E cua day hinh ndn ke dudng cao SE - Mat phing trung true ciia mdt dudng cao bat ki cat SE tai O Chiing minh O la tam mat cau ngoai tiep hinh chdp Bai Hudng ddn - Chiing minh tam I dudng trdn ndi tie'p tam giac ABC thudc mat cau dd - Chiing minh ABC la tam giac deu - Chiing minh SI (ABC) Bai Hudng ddn A 36 a) HS tu giai Tfnh HB = r = 1V3 - Dudng sinh khdi tru a Bai Hudng ddn Ke mat phing trung true cua SA cit SO tai I Chiing minh I la tam mat ciu De tfnh r = SI ta su dung tam giac ddng dang SI SE „ SE.SA — = — ^ SI = SA SO SO Bai HS tu giai Cau hdi trac nghiem : HS tu giai 37 HOATDONC MOT SO D^ KI^M TRA CHUONG H De sd Cdu i ( d) Cho hinh hop chii nhat ABCDA'B'CD' canh a, b, c a) Xac dinh tam mat cau ngoai tie'p hinh hop b) Tfnh dien tfch mat cau dd Cdu (4 d) Cho hinh ndn cd ban kfnh day la 4, dudng cao la a) Tfnh dien tich xung quanh va the tfch hinh ndn b) Tfnh ban kfnh hinh cau ngoai tiep hinh ndn dd Cdu (3d) Cho hinh tru cd ban kfnh day la 4, chieu cao Cit hinh tru bdi mot mat phing song song vdi true a) Hinh thiet dien la hinh gi? b) Neu cac dung hinh dd biet hinh dd cd dien tfch la 18 De sd Cdu i d) Cho hinh cau cd ban kfnh la a) Tfnh the tfch khd'i cau va dien tfch mat ciu b) Tfnh the tfch hinh tru ngoai tiep hinh cau Cdu (4 d) Cho hinh ndn cd ban kfnh day la 6, dudng cao la a) Tfnh dd dai dudng sinh b) Mdt mat phing vudng gdc vdi true cit hinh ndn theo mdt dudng trdn ban kinhd la Tfnh the tfch hinh ndn cut tao 38 Chi/ofNq PHlTOlVG P H A P I W A T R O a f G HHOIVG GIAIV Phan Gidl THlfu CHUOHG I CAU TAO CHUONG § He tpa dp khdng gian § Phuong trinh mat phing §3 Phuang trinh dudng thing khdng gian On tap chuang III On tap cud'i nam Muc dich ciia chuong • Chuong III nhim cung cap cho hpc sinh nhiing kien thiic co ban ve khai niem ve tpa dp khdng gian va nhiing ling dung ciia nd Tpa dp vecto va tpa dp diem - Bieu thiie tpa dp cua cac phep toan vecto Tfch vd hudng cua hai vecto Phuang trinh mat cau • Gidi thieu vd phuang trinh mat phing khong gian Vecto phap tuyen cua mat phing - Phuong trinh tdng quat ciia mat phing - Dieu kien de hai mat phang song song, vudng gdc Khoang each tir mot diem den mdt mat phing 39 • Phuang trinh dudng thing khdng gian: Phuang trinh tham sd cua dudng thing - Dieu kien de hai dudng thing song song - Dieu kien de hai dudng thing cheo - Dieu kien de hai dudng thing cit II MUC TIEU Kien thurc Nam dupe toan bd kien thiic co ban chuong da neu tren Hieu cac khai niem va tfnh chat vecto khdng gian Hieu va bie't dupe mdi quan he giiia vecto phap tuye'n va cap vecto chi phuang ciia mat phing Hieu va biet dupe mdi quan he giiia vecto phap tuye'n va vecto chi phuong ciia dudng thing Kl nang Xac dinh dupe cac vectp khdng gian Van dung dupe eac tfnh chit de giai bai tap - Chiing minh dupe hai mat phing, song song, vudng gdc Lap dupe cac phuang trinh dudng thing va phuang trinh mat phing Xac dinh dupe vi tri tuong ddi cua dudng thing va dudng thing, dudng thing va mat phing, giiia hai mat phing Thai dp Hpc xong chuang hpc sinh se lien he dupe vdi nhieu van de thuc te' sinh ddng, lien he dupe vdi nhiing van de hinh hpc da hpc d Idp dudi, md mot each nhin mdi ve hinh hpc Til dd, cac em cd the tu minh sang tao nhCrng bai toan hoac nhiing dang toan mdi Ket ludn: Khi hpc xong chuong hpc sinh cin lam tdt cac bai tap sach giao khoa va lam dupe cac bai kiem tra chuong 40 ... chat ciia tie''p tuye''n mat ciu HS tu giai Bai Hudng ddn HS tu giai Bai 10 Hudng ddn HS tu giai 27 On tap churdng II (tiet 11 , 12 ) MUC TIEU Kien thurc HS n i m duac: Khai niem chung ve mat trdn xoay... dudng sinh va dudng cao cua hinh tru Cdu hdi 10 Neu dinh nghia mat ciu bing cac each khac Cdu hdi 11 Hinh cau va mat ciu khac nhu the'' nao? Cdu hdi 12 TCr mdt diem ke hai tie''p tuyen de''n mat... hinh chdp bing : (a) 4 71 r^ V3 ; (b) - 71 r^ V3; (c)4r''V3; (d)3r''V3 Trd Idi (a) Cdu 15 Cho hinh ciu S(0 ; 4) nhu hinh ve AB bing : (a)2V3; (b)3V3 (c)3; (d)6 Trdldi (a) Cdu 16 Cho hinh cau S(0 ;