vuong c4ch a, M 1d trung ciiem cua AB,m[t phing SAB li tanr giac diu ruong goc r'cri day.. Th€ tich khoi chop S.ABC \i.. g6c giira m[t phing scD vd m7t phing ABCD ld ooc... Tinh th6 tich
Trang 1Nim hgc 20t6 -2A77
't \",* L*
ox r4.r: TIIIE ricu KHOI EA rIIEN
***
CAu 1: Cho hrnh chop S.ABCD co (SAB) vd (SAD) cing rT r6ng g6c (ABCD) ducmg cao kh5i ch6p
S ABCD 1d:
CAu 2: C.ho hinh chop S.ABCD day ld hinh vuong c4ch a, M 1d trung ciiem cua AB,m[t phing SAB li tanr
giac diu ruong goc r'cri day Ducmg cao kh6i chop S'ABCD ld:
DSM
CAu 3: 6fitr lang tru ABCD A'B'C'I)' hinh chicu vuong goc A' l6n ABCD trung vcn tmng I di6m AC'
ducrng cao khor lin-s tru ABCD 'A'B'C'D' ia:
Biot Sl t(ABCo) vh S-4 =r'Jj
D ar./r
12
A ,t.,6
cau 5: Clho hinh chop s.,4BC co rtdy .4llc latam gidc d€r.t canh a 5-.{ i (Afi()
":2 sl = a.,,6 Tne tich khdi chop S.ABC 1ir:
Cflu 4: Cho hinh chop S.IACD co day AtsCD li hinh vuong cqnh a
tich cua khol chop S.-ABCDlil'
D SD
3a'
D-6
,AC =2a SA:GBQ vir
(")+ Aa' ,/4
n)
B."
4
tG (c)o"
J
3a)
('= cAu 5: Cho hinh chop s.l{Bc co d6-v ABC lirtam gid:c vuong can tai r bi6t
SA = aJ1 Th€ tich khoi chop S.ABC \i '.
r3
^3Q
A
-1
r \:(,I
l-\
8
c, "6o'
CAu 7: Cho mot khoi chop co the trch bing l' Khr gram diQn ttuh da gia(- dai xuong
,,!
3
, t.
a l)
t)
-3
- lan thl '.1).- '.1rrI Kili'i
J
chop iuc do bing:
CSu g: Cho kh6i 16ng tru ABC.A'B'C' co the tich la ,', thO tich cua tchOi ctrOp C''ABC la"
tlit
c6u 9 : Ciro hinh chop S.ABCD co d6,i,'ABCD lh hinh vuSng c4nh a c4nh ben SA vuong goc voi m6t
;l15n* dt.;"a6 ,oo r,oi m[t d6y m6t goc bing 600 Tinh th6 tich khoi ch6p S.ABCD
:"'366
C6u 10: Cho hinh ch6p S.ABCD co d6y lir hinh chu nhat Viri AB = 2a, AD = a' Hinh chieu cua
S l6n (ABCD) la trung dicm H cua AB, SC tao voi dd.v mot g6c 45o.Th6 tich kh6i ch6p S'ABCD ld:
Ciu ll: Cho hinli chop S.ABCD co da5 lir hinh ruong c?nh a tim O' hinh chieu cua !]$.l.tte'
;il G* i,o,ecoi td trung diem cua Ao g6c giira m[t phing (scD) vd m7t phing (ABCD) ld ooc iintr 1ne tictr cua kh6i ch6p S.ABCD
c6u 12: t.lro hinh ch6p s.ABCD co diry ABCD ld hinh .t6ng Mat b€n sAB liltam gi6c ddu canh a va nlm
;;;G;[Lng vurng gtic vcri (ABCD1 The tic]r cua khdi ch6p S.lBLiD li:
LrAi n n7"/11 l7^1 6
Trang 2A o'Ji B a'Jt c n'
Cflu13:ClhohinhchopS.4S(.Dcoddy-ldhrnhchiinhdt canhAlJ==2a.AD='.r.caccanhh6nd€ucodqldai bing 3a Th6 tich khoi ch6p t.-4l9{-1f bing
,1-i
9 , '"6
9 Ciu 14: Cho khoi chop 5 48C co .S.4 r.udng goc rro'i IABO tld1,-.1.tsC" la tam giac w6ng cin tai ,4 BC:Ja.
goc gifra SB i,a (ABC) ld 30" The tich khoi chop S.lBtl iii:
iA.:-:: g 1-lI C.''"" I),
''-9354
CAu15: Khdi chop S.ABC crj-.57r'u6nggocr,di (.48C).day.4Bt: iatamgr6cr,uongtai B.Bict,\B:7o.BC
: a v0 th6 tich kirtii ch6p la n' Khoang crich tu l ddn (^SACI la:
D t*"
-Cffu 16: Cho hinh ch6p dAu S ABCD co canh ddy 2a g6c giira mit bdn vi mit d6y bAng 60u Tinh th6 tich cta khdi chop S.ABCD .
7f:.tfa
A df B 1u f, c 2,_s D 4Jja,
333
CAu 17: Cho hinh ch6p S.ABCD c6 ddy ABCD ld hinh vu6ng c4nh a MAt ben (SAB) ld tam gi5c ddu vd
rudng g6c vdi d6y.Th0 tich k&iii chdp S.,4BCD ld
A o'J1
r/l
o0v''
D
2336
Ciu 18: Cho hinh ch6p S.ABCD d6y H hinh thoi voi AC:2BD:2avdtamgi6c SAD w6ng c6n t4i S nim
trong mp vu6ng g6c voi d6y.The tich kh6i ch6p 1i:
,' '.! ia
12
r;:
, v-.a
CAU 19: Chohinh ch6pS.ABCDc6diryABCDldhinhchtnh$t c6AB: (r,BC -20 Haimp SAB vit
mp SAD cirng vu6ng g6c voi m[t phing d6y, c4nh SChqp vcri'd6y m6t g6c600 Tinh th0 tich kh6i
chop S.ABCD theo o
e.zu'Ji B a'Jis c 2a'JG o.zu'Ji
333s
Ciu 20: Cho hinh ch6p S.ABC co ddy ld tam gi5c ABC vuOng tpi B AB : oJi, SA vuOng g6c vdi d6y vi SA: i Tinh khodng cach tu diem A dOn mp(SBC)
2
A.D (_
t;
D o'"1 '
6
Cflu 21: Cho ldnh ch6p -e.ABCDcd, da1' ABCDIi)hinh r,u6ng canir tr , ,5.4 -L .18(D vA mit bOn SCI) hop vcri m[t phing d.iry ABCDmot gi'rc 6i]" Tinh kho6ng c6ch ff rli6m zi d6n rnp SC? .
-
3322
-Chu 22: Cho hinh ch6p S^IBC co 5C' .- "{t d,at' -4BC lir tam giac ru6ng tai A AB : 2a 4C : o ya
o
hinh chi6u cua S l6n mdt phdng lABC tla trung di6rn H cua canh lB Tinh khoang c6ch grfa hai ducmg
t:
.4
1
B. a 4
4
C -rl V:
A
D.ia
5
thEng BC va.!l: A.
f6 Toin - Trud.ng THPT TrAn Qrfiy Cip - Tp HOi An
Trang 3Ot'tgp c Nim hsc 2016 - 2017
CAu 23: Cho kh6i ch6p S.,4BC co SA vnong goc voi d6y', tam gi6c ABC vuong cAn taj B, SA : a SB hqp
roiddy goc 300 Tinl khoang c6ch giira AB va SC.
r:
^vJ
5
J
)
lt
Ciu 24: Cho hinh chop S.ABCD co da-,- ABCD lir hinh chfr nhAt co AB : rJI BC : 2a SA r,r-r6ng goc r'di d6,v G6c gita nr6t b6n (SBC) r,a m6t da-v bing 60f' Tfnh theo a th€ tich khOi chop S.ABCD
.,/Tn,[1
3-339
Ciu 25: Cho hinh chop S.ABCD co d6-v ld hinh thoi tam gi6c SAB d6u vir nim trong m[t ph6ng vuong goc vcri day Bi6t AC:2a BD=3a Tinh khoang c6ch gifta hai dutmg th6ng AD va SC
r Do8
A _ .l_a
2Y:17 Ciu 26 Cho khdi chop S 4BC co th6 tich ld tz- Gqi B', C'lAn 1uo't la trung dr0m cua .48 vit AC Th6' fich cua
kh6i ch6p S.AB'C ' sE li:
xlv e li
^t
/-)
rll
SA': ISA: SB': 1SS: SC': lSC Gstl, vh l''lAn luot ld th6tichcuac6ckh6ichop S.ABCvit
234
S.A B'C' Khido r, rO I la:
l/
B 1
12
Cflu 28 : Cho hinh chop S.AB(lco d6y ld A4BCvuong cin o B -4C : ,.8.5.'1 i :n4r ABC .5-4 : a
Gqi Gldtrqngtdmcua 4.5'BC, mp L\ dtquaAGvdisongsongvoi BCchtSC.SBldnlugttailul,A.Tinh th€ tich tnOi ctrOp S.AIIIN,
3-272799
Ciu 29 : Cho hlnh ch6p ru giric S.ABCD c6 th6 tich bing Y LAy di€m A' tr6n canh SA sao cho
1,1
SZ'= i^Sl Mat phing qua A'vir song song voi d6y cua hinh chirp c[t c6c canh SB, SC, SD l6n luot t?i B',
,
d
c" D' Khi d6 tho tich ttr6i ctrop s.A'B'c'D' bing:
Ciu 30: Cho khdi i[ng tr.u ABC.A'B'C' ca the tich ld ,a th6 tich cua ttrOi ctrOp A.BB'C'C ld:
t
B :_V
4
c Lr,
4
c.24
3
Di
24
olv
6
n lrz
6
d ?v
3
Ciu 3l: Khi ting da dai tAt ca c6c c4nh cua mat khoi hQp chfl'nh6t len g6p d6i thi the tich khoi hQp tuong img sE:
A t[ng 2 l6n B ting 4 lAn C tang 6 i6n D t[ng 8 lan
Cflu 32: N6u ba kich thuoc cua mOt t<hOi cnt nhat t619 16n 4 ldn thi th6 tich cua n6 ting 16n:
Cflu 33: Cho mQt ttrOi tap phucmg biet ring khi ting dq dAi canh cua t<trOi tap phucmg them 2cm thi the tich cua no ting th€m 98cm3 Hoi canh cua kh5i 16p phucmg dE cho hing;
Ciu 34: 'tong diQn tich cdc mbt cua mdt hinh 16p phuo'ng b[ng 96 cm t .Th6 dch cua
t<irOi tap phuong do ld:
[rA: i.- fr2,tr1l1n1K
1-HH 12
Trang 4t6 fo6n - Truirng THPT TrAn Qriy Cip - Tp Hgi An
Cflu 35: X.l6i cirop S.ABCD c6 th6 tich ld V Gqri \{ N lin luc,'t 1., trung dr0m cua SC, SIl Thi rich cua
kh6r ch6p S.ABMN 1A:
1r
Cflu 36: Th€ tich cira kh6i ch6p tam gidc d6u cti tit ca cdic canh deu bing c 1Ạ
_-7
ụ ạ-
-Cf,u 37: Cho hinh ling tru deu ABC a r9'C'cir canh da,v bine c canh ben bing J.: The tich cua khoi lang tru iir:
p.:-:E!
CAu 38: Cho hinh l6ng tru tam gi6c diu co cac canir deu bang a Tir0 tich khoi lang tru di:u la:
^ r /^
^ /.a
1/-Ạ
a
.;
Ạ á3
Ạ ot
48
E
B atr
B ,,
3
7
L a-
-b
')
^-l
L._
J
zli
D.4-vs
4
Cf,u 39: Cho kh5r thng tru tltmg tam giac AB{'.A 'B'C cri đ1,la nrOi tar.n gi6c ruong cin tar l Cho
AC = AB =2ạ goc giiralC vi nrdt phbng ienf yAang 3l)r Tha rrch khor lAng trp ABC 4 'B'f '14
^ +a!3 17 *=-_JaiJ
ạ
J-1
4áJj
J
Ciu 40: Cho ilng tru dung ABC.ÁB'C'c6 d6y ABC le hm giitc vu6ng tai B AB :2a,BC: ạ
AÁ :ZaJ1 Tinh theo a the tich ttrOl tang ffu ABC.ÁB'C' .
^rE
^ :a 1/-1
-)
.r
a""lJ
CAu 41: Cho l[ng tr,u dung AtsC.ÁB'C' cb dity ABC H tam gi6c vu6ng tai B AB :alr,BC :3ạ G6c gifra canh ÁB vd mlt dity le 600 Tinh theo a th6 tich tnOl tang tv ABC.Á B'C' .
Ciu 42: Cho llng tru dung ABC.ÁB'C' co dly ABC la tum gsitcdAu canh '3 Ị CỌ gita m[t (ÁBC)vitm{t
d6y ln 450 Tinh theo a th6 tictr t<trOi Ung tru ABC.ÁB'C' .
B ó
3
1
D a-16
CAu 43: Cho ABC'D.ÁB'C'D' 1i, hinh lpp phucrng co cpnh a " Ihe i jch cua kh6i trl di0n ICD ,B' bing :
-r"
B 1-L'.
3
á
Ạ-J
l
c."
4
t- :
^!54
L.-4
Cffu 44: Cho hinh ldng tru ABC.ÁB'C' d6r, la tarl giac đu cach ạ cach ben bing ậ,6 va hq? da,v b5ng
OO0 TUe tich cua t<trOi tang tru bing:
ụ 3.6r, b jf'
, Jig- d .'S"
628
Ciu 45; Cho hinh llng tm ABC.ÁB'C' day ld tam gi6c đu cach ạ hinh chi5u vuong g6c Á len đy trung vdi tim duong tron ngoai ti6p tam giac ABC r'ir ÁA hop đ,v bing 60(' Th€ tich cua khoi l6ng t4r
^ vja
4
ABC.ÁB'C'bing: Ạ 3J6r'
rrAi a- A2/t1/"'nt(