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






./012345,62
7

012345899:2


0123459;8-
7 7 7
a b c
+ +
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
7
a
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,@A-$(2$<,5B,4CD'2E&4$(
F/GH2DI<,H2DI 2-$(2$<,
BÀI TẬP
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@B
a
"
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 MNOD,2%&4"OL
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
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2;"$(@PFQ
U
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U
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2-SU
U
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B. MẶT NÓN, MẶT TRỤ, MẶT CẦU.
I) MẶT NÓN, HÌNH NÓN, KHỐI NÓN:
1) Mặt nón:
12J2∆l,i
2-α@UmαmWU
U
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d(YDX12J2f,(
f,12J2∆2N&A-
* d: đường sinh
*
∆
: trục
* O đỉnh
* 2
α
: góc ở đỉnh
2) Hình nón:
=5-Dnd(5YDX&
&2$,62f,(f,&
2-,62
oDiện tích xung quanh:"
df

π
Dl
l: độ dài đường sinh
r: bán kính đường tròn đáy.
3) Khối nón:
=5-'29*D24-

r: bán kính đường tròn đáy.
3) Khối trụ:
=5DI'29*D24-
+2NDI
oThể tích khối nón: D
7

h: độ dài đường cao
r: bán kính đường tròn đáy
 Chú ý: DIl.
III) MẶT CẦU, HÌNH CẦU, KHỐI CẦU:
1) Mặt cầu:
%&ikYqD
K89+9$%&[D2622
$%&i&p2?2D+
2N&A*,E&i$D
r!,"@iD
{ }
Di[[
=
Chú ý: oisD
⇔
?&2@"
oimD
⇔
?&D2@"
oiD
⇔
?&D>@"
2) Vị trí tương đối của mặt phẳng và mặt cầu:

∆B9du@"=
r-∆: tiếp tuyến(H): tiếp điểm
omD
⇔
@tl@"%&9E!
Q
FP!d,2f,5*,%*,
oP!d,2f,5*,"
df
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
F
π
D


BÀI TẬP
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K!d,2f,45-]
K%4-
[B!f,C45--p2$RE&4$(B&A9J2 B!.7
&K!B!-
7[5DI-$$(DQ&-p2$2;$(?2T&
K!d,2f,45DI%4DI
lDIX&A9J2Y2Y2-DI$DI&K!4B!+

W[ !<,-?2B9D2&-K%4--
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= +

a)Viết phương trình mặt phẳng (P) chứa (d
1
) và song song (d
2
).
ĐS : 2x – z = 0
b)Cho M(2;1;4) .Tìm toạ độ điểm H thuộc (d
2
) sao cho MH nhỏ nhất ?
ĐS : H(2;3;3)

c.Qua C(2;-1;5) và
3 1
2
2 3
x z
y
+ −
= + =
.
ĐS: x +7 y – 3z +20 = 0
VB9:2D5&A9J2$<,12J2
.

7
B

.
7
 7

x t
d y t
z t
= +


= +


= −

a.Chứng minh : (d) // (d’) .
b.Viết PTmp chứa (d) và (d’) .ĐS : 10x + 16y – 17z + 72 = 0 .
SKD2622!DINid(x12J2∆
. 
. . F
x y z− −
= =
%&[@Uy~7yUB
9:2D5&A9J2@tf,%&[Y2Y212J2∆w21p2$2;12J2∆
&A9J2@t?2F
ĐS:4x - 8y + z - 16 = 0. Hay 2x + 2y - z + 4 = 0.
.7
3. Quan hệ giữa hai mặt phẳng
Qj3kD:24$A9&A9J2X$9:2D5Y,
d•(€7x•FU.Ud•.U(€7Ux•FUU
7d•d•x€QWd•S(•Wx•QU
d€(€x•.U7d€7(•7x€U
S&A9J2-9:2D57d•&(€x•SU@&€d•7(€@Q&€.x•.UU
2$Dk4&5&A9J2-
"2Y2,
KD'2,
l,,622-,
4. Một số bài tập liên quan khác
.D22!Nid(x%&@.Uy7y~.12J2-9:2D5





+=

](B9:2D54&A
9J2-p2$B@Pv
ĐS:
7d~x~WU
.
%&
( )
7yQyA
12J2
. 7
 
7 . 7
x y z
d
− −
= =
B9:2D5&A9J2
( )
α
 
d
Y
p2$R
A
B
( )
α
v.
ĐS:
7 7 .Q Ux y z+ + − =

∆ = =
− −
B9:2D5&Y412J2f,%&Olp12J2
.
∆

7
∆
B9:2D5&A9J2@
α
f,%&OY2Y2
.
∆

7
∆
ĐS:9x + 5y -2z – 34 = 0
T%&
( )
7yQyA
12J2
. 7
 
7 . 7
x y z
d
− −
= =
B9:2D5&A9J2
( )