B
h
a
b
c
a
a
a
B
h

 THỂ TÍCH KHỐI ĐA DI Ệ N
I/ Các công thức thể tích của khối đa diện:
1. THỂ TÍCH KHỐI LĂNG TRỤ:


B: dieän tích ñaùy
h : chieàu cao





 Thể tích khối hộp chữ nhật

 !
 Thể tích khối lập phương

"

#$%&

Chú ý:
56!789':;8&%


6!789':<==!>8&%
"

6!789':$=?<4" !%
  
a b c
+ +

56!78':.8,#@&
"

a
"54=#@4=4#,0#8,#@,&A#@B8
C'D4#,0#8,#@:#EF/8G.:#,0
H5IJ8FK#@J8FK#84#,0#8,#@
BÀI TẬP
''=*4#,0.8,;8&#!78L8*;884.=
C
"a
*"
 M - (4=*N'
 OPF8#-.:&* #$%#'&PN'
'4=.8,#@*4&#,0B8&AB8OPF8#-.:

 8.*;884
 M - (4=*PN'

#,0CQ*Q
M - :(4=*Q
''=*Q4#,0;8&*;884.D#,0CQ84
8?*#,0CQHR
V
M - :(4=*Q
'(4=*4#,0.8,;8Y6E*,#@.D
AC*3=.D#,0C84TV
V
M - (4=*
Q

"'(J8FK+++4#,0.8,#@&B8&AB8
"a

C;884:+ACF/8F8#-.:M - (J8FKS#4Z0
F- :(4=+
Q
H'(J8FK.8,+++4#,0.8,#@&B8&A3=#,0
84TV
V
+,#@8.++?< - :(J8FK
+++
Q


R'J8FK#8+++4#,0.$.8,;8&
·
V
TVACB =

A
`
+
a
8'
`

b

+>
`
.J
_
#
`
0J
a
8
α

\c8C8C+
a
d
`
A
b
d
`

b

+++'
`
#
`
0
a
.8
`
#A
a

_

_
A+G#!>
a
8;8
8'
`

_
!
a
+e;
`
8#
`
0F
a
8>

J8F
_

\c.J
_
A++
a
d
a
!
f
G
_

Xd
a
J8F
_
#!
`
8+++'
`
#
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0
a
.8
`
;8
_

#;
_
%
a
#'
_
+
Md
`
A
b
d
`

b
J8F
_

V';
`
;
_
=Q+++Q+'
`
G
`

b

`

`
;
_
=#'
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N'
';
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J8F
_
+++'
`
#
`
0
a
.8
`
#A
a

_
#A
b
.+
`
#A
a
#A
b

#'
`

\c.J
_
A++
a
.;
_
d
a
!
f
G
_

Md
`
;
b
8%A
_
d
`

`
.J
_
A
b

b
8#g\+
;
`
J8F
_

a
=G
a
Md
`
d
b
Z;
`
A
b
d
`

b
=G
a
#'
`

"'d
a
J8F

%A
_
++
\J
_
=J
b
8#g++
a
F'
_
8G..8
`
J
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
a
G
a
!>
_
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h
a
iMd
`
A
b


a
A
b
d
`
;
`
;
_
=
R'd
a
;
_
=Q+++Q+8'
_
j
a
8'#A
b
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B. MẶT NÓN, MẶT TRỤ, MẶT CẦU.
I) MẶT NÓN, HÌNH NÓN, KHỐI NÓN:
1) Mặt nón:
'#!78L8∆%m&j
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V
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g#!78L8∆8.D4
* d: đường sinh
*
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: trục
* O đỉnh
* 2
α
: góc ở đỉnh
2) Hình nón:
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.8,;8g0g.$&
84;8
H
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pDiện tích xung quanh:*
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l: độ dài đường sinh
r: bán kính đường tròn đáy.
3) Khối trụ:
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#!38(FK
pThể tích khối nón: F


h: độ dài đường cao
r: bán kính đường tròn đáy
 Chú ý: #((FKl.
III) MẶT CẦU, HÌNH CẦU, KHỐI CẦU:
1) Mặt cầu:
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s#4∆: tiếp tuyến(H): tiếp điểm
p%nF
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pQ) e8g2*
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BÀI TẬP
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2
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