100 bài tập hình học không gian 12 nâng cao

Bài 1: Cho lăng trụ đứ ng ABC .A’B’C’ có đáy ABC là một tam giác vuông tại A , AC = b ,  0 C 60 .Đường chéo BC’ của mặt bên BB’C’C tạo với mp (AA’C’C) môṭ góc 0 30 . 1/Tính độ dài đoạn AC’ 2/Tính V khối lăng trụ . Bài 2: Cho lăng tru ̣ tam giác ABC .A’B’C’ có đáy ABC là môṭ tam giác đều caṇ h a và điểm A’ cách đều các điểm A ,B,C.Cạnh bên AA’ tạo với mp đáy một góc 0 60 . 1/Tính V khối lăng trụ . 2/C/m măṭ bên BCC’B’ là môṭ hình chữ nhâṭ . 3/Tính Sxq hình lăng trụ . Bài 3: Tính V khối tứ diện đều cạnh a . Bài 4: Cho hình ch óp tứ giác đều S.ABCD. 1/Biết AB =a và góc giữa măṭ bên và đáy bằng ,tính V khối chóp. 2/Biết trung đoaṇ bằng d và góc giữa caṇ h bên và đáy bằng  . Tính V khối chóp . Bài 5:Cho hình chóp tam giác đều S .ABC. 1/Biết AB=a và SA=l ,tính V khối chóp . 2/Biết SA=l và góc giữa măṭ bên và đáy bằng ,tính V khối chóp. Bài 6: Hình chóp cụt tam giác đều có cạnh đáy lớn 2a, đáy nhỏ là a, góc giữa đường cao vớ i măṭ bên là 0 30 .Tính V khối chóp cụt . Bài 7: Môṭ hình tru ̣ có bán kính đáy R và có thiết diêṇ qua truc̣ là môṭ hình vuông . 1/Tính Sxq va Stp của hình trụ . 2/Tính V khối trụ tương ứng . 3/Tính V khối lăng trụ tứ giác đều nội tiếp trong khối trụ đã cho .

1 1: Cho     .      , AC = b ,  0 C 60 . ()      0 30 . 1/  2/ . 2:      .                       ,B,C. 0 60 . 1/ . 2/C/             . 3/ xq S . 3:  . 4:   .ABCD. 1/=              ,. 2/                . T. 5:       .ABC. 1/=  =l ,. 2/=              ,. i 6:  2a,       ,         0 30 .. 7:                               . 1/ xq tp S va S . 2/ . 3/ . 8:                    R3 .    2   2                          0 30 . 1/ xq tp S va S . 2/ . 9:                          . 1/ xq tp S va S . 2/   . 10:              . 1/ . 2/. 3/  . 11:                    ,      0 60 . 1/ . 2 2/ 3/ . 12:          =        .    ,   = x (0<x<h). 1/ ()         . 2/  () theo R ,  .            ? 13: .      ,   . 1/ . 2/  tan  . 14:            =            .                         . 1/ . 2/ xq S  . 3/ tp S . 15:      .    ,ng   ()   . xq S  . 16:    .           . (ABC)    .Cho  0 BAA' 45 . 1/C/         . 2/ xq S . 17:           .            ASB  . 1/ xq S . 2/C/         : 2 a cot 1 22   3/  .c   5   S,A,B,C,D. 18:     .           ,            0 60 .. 19:   .         cân ,AB=AC=5a ,BC =6a ,              0 60 .. 20:       .           .nh SA       .           AD SB, AE SC .=a, BC=b,SA=c. 1/.ADE. 3 2/ (SAB) . 21:              1       1      1   . 22:          .  AB =a,BC =2a ,=a.      AM =3MD. 1/  2/  23:          .  =a,BC =b ,=c.,N              . .DMN        24: Cho 2          ,         .=h, AB =a, CD =      2        0 60 .. 25:     .(H)                . ABCD V(H) V . 26:  . 27:      . 28:      .  29:     .ABC.      ,SB,  3   , ,     .C/m : S.A'B'C' S.ABC V SA' SB' SC' . . . V SA SB SC  30:        .  =a .,SB,            0 60 .. 31:        .ABC =5a ,BC=6a ,CA=7a. SAB,SBC,           0 60 . . 32:     .             ,         =a ,AD=b, SA =c.    ,      ,SD sao cho AB' SB,AD' SD .    ()   .. 33:          .ABCD ,         ,  0 60 .    .         ,      . S.AEMF. 34:          .        . 1/  . 2/         ABC ,          F. 35:      ... ,       BC. 1/. 4 2/    (DMN)        2   .(H)        ,()  . (H) (H') V V 36: Cho   .    =a ,         AB =BC =a.  ,           ABC . 1/ .ABC. 2/C/m : SC mp(AB'C') . 3/ 37:   .    = 2a , ABC     =2a,  0 CAB 30 .,           . 1/   .ABC. 2/C/m : AH SB  SB mp(AHK) . 3/ .AHK. 38:        .               =a ,BC =2a ,=3a .  (P)          . 1/  2/C/m : AN A'B . 3/ . 4/ AMN S  .  39:   .        2a ,         , AB =a, AC a 3  (ABC)  ..       2        40: C    .         2a ,SA=a , SB a 3 (SAB)            .,       ,BC . .   2     ,DN. i 41:    .         ,AB=BC=a,  AA' a 2 .       . .        2       42:    .           ,                    .,N,             ,BC,CD.C/m : AM BP .  43:         .           .             ,        ,       . C/m : MN BD  2       . 5  44:    .         ,   0 ABC BAD 90 , BA=BC=a ,AD =2a. SA a 2 .      . C/m SCD vuông    d H;(SCD) .  45:            2  ,    .         ,          = 2a ..  46:    .     =a , AD a 2 ,SA=    SA mp(ABCD) .,           SC .        . 1/Cmr: mp(SAC) mp(SMB) 2/   .  47:       .           , SA =2a  SA mp(ABC) .,                   .A.BCMN. B 48:          .  ,      qua 2  1  0 60 ..  49: 1  ;                  1   ..  50: Cho 1  .      =              1    1   . .  51: 1  1   .  .  52:     .         ,= a .            .             . 1/C/           . 2/.  53:          .      1  .   . xq S .  54:        .ABC .            ,            1   .           0 A 90 ,  0 B 60 , =a.  xq S .  55:            .  1     AB=AC =    A2 .  3   ,B,      ( ABC)   .  xq S     . 6  56:              1    .        ,A,        (ABC) 1    1   ..  57:          .                 , .  ASB = 2    00 0 45   .  xq S .  58:     ..        =AC = 0 120 .  .  xq S .  59:      .             AC =    C  .()        ()     ..  60:     .           ,  A  ,             (ABCD)      .=a . xq S .  61:     .           ; (SAC) vuông ;  0 ASC 90 1   . .  62:     .     0 BAC 90 ,ABC   ;         (SAB) (ABC) . .  63:          .ABCD , , 2  . xq S .  64:     .               SA=SB=SC =a .h   d S;(ABC) .  65:     .           a3 ,    SA=a.               .  AHK S  .  66:     .ABCD ,                  2 a3 2      0 60 .                1  0 45 . 1/              . 2/  .  67:     .ABCD ,            ,AB=BC=2a ;            =2a . 1/  . 2/  .  68:     .    =x , 1. 1/C/m: SA SC 7 2/ .  69:     .ABCD .             =BC=CD=a = 2a .           ,mp(SBD)    1  0 45 . 1/ . 2/   d C;(SBD) .  70:       =a ,BC =b, BD =c,   0 ABD ABC 60 ,  0 CBD 90 ..  71:        BC.,         c,      (ABC).(        ),    (ABC) 1   .  BC 2/   .  72:          .        . 1/ .ABCD . 2/ .  73:       .ABC, =1   26 .  ,         ,  . .                .  74: Trong mp(P) cho 1     1            =h .     ,C sao cho   0 BOH COH 30 .          (P) ,   =OB . 1/. 2/   d O;(ABC) theo h .  75:     .    =           1 . 1/C/m : SA SC . 2/. .  76:  , =a, AC=AD=BC=BD=CD= a3 .  77:           =SB =SC =    0 ASB 90 ,  0 BSC 60 ,  0 ASC 90 . 1/C/m : ABC . 2/.  78:        ,    0 BAD 60 . AB' BD' .     .  79:            =2R , 1       .   CH AB (  )  .           (ABC)     0 ASB 90 . 1/C/m : SHC . 2/=h . . 8  80:       3 ,AC,AD,          AB=a, AC=2a ,AD =3a . .  81:      .      .          (ABC)  2IS a 3 . 1/C/m: SAD  . 2/ .ACD. Suy ra   d C;(SAD) .  82:          1  2   ,  1 , 2                2 .                 1  0 45 . xq S .  83:     ,               0 A 120 .         (ABC) ,    SA= a3 . 1/   . 2/Cho R =2a,  . trên mp(ABC).  84:     .ABCD ,            =2a, BC=a, .        a2 . .ABCD theo a.  85:       , AC,            , AB=a, AC=2a ,AD=3a. 1/   d A;(BCD) 2/ BCD S  .  86:         .  ,  =h. 1/ . 2/ .ABCD .  87:         .           ng a.   ( 00 45 90 )   . TP S .  88:     .           2a. = a5 .   (P)        (SCD) .(P)          . 1/ 2/   89:   .    2      ,    . .  90:         .          =      SAB  . .    .  91:     .           . =2             . 1/ TP S . 9 2/ SB , AF SD . C/m: SC mp(AEF) .  92:         .             =SB =SC= =SD =a. TP S .ABCD .  93:   1     1        =2a ,  mp(ABC) =a. 1/   d A;mp(SBC) . 2/.   d O;mp(SBC) .  94:          S.             D , AB=AD =a ,CD=2a . mp(ABCD) ,SD= a . 1/C/mr: SBC vuông . SBC S  . 2/   d A;(SBC) . i 95:     .             ,=2a ,BC =a ,  a2 ..  96:         .              D , AB=AD =a ,CD=2a . mp(ABCD) ,SD a3 .      SC (K SC) ..   SC mp(EBK) .  97:     .         . SA (ABCD) , SA= a6 .       . 1/C/m : AH (SBC) 2/ .   d O;(SBC) .  98:         .             D.=2a ,AD=CD =a (a>0). =3       . 1/ SBD S  . 2/.  99:                  ,   1         a2 . xq S , tp S .  100:        .           .        .                Sc. =a ,BC =b, SA =c . 1/.ADE. 2/   d E;(SAB) . . 1/ . 2 2/ 3/ .  12:          =        ..     ..        =AC = 0 120 .  .  xq S