15-5.立体の容積および諸数値
V=容積，S=表面積，A
s
=側面積， A
b
=底面積，x=底面より重心までの距離
寸法
容積および諸数値
寸法
容積および諸数値
正方体
a=
d=
V=a
3
=
S=6a
2
=
A
s
=4d
2
=
x=a/2=
d=3
0.5
a=1.7321a
=
正多角形
a=辺長=
n=辺数=
A
b
=底面積=
h=高さ=
V=A
b
h=
S=2A
b
+nha=
A
s
=nha=
x=h/2=
長方体
a=
b=
h=
V=abh
=
S=2(ab+ah+bh)
=
A
s
=2h(a+b)
=
x=h/2
=
d=(a
2
+b
2
+h
2
)
0.5
=
円柱 中空円柱
h=
r=
R=
t=
As=
V=πr
2
h
=
V=A
s
h
=
S=2πr(r+h)
=
A
s
=2πrh
=
x=h/2
=
V=πh(R
2
-r
2
)
=
V=πht(2R-t)
=
V=πht(2r+t)
=
x=h/2
=
正六角柱
a=
h=
V=2.598a
2
h
=
S=5.1963a
2
+6ah
=
A
s
=6ah=
x=h/2=
d=(h
2
+4a
2
)
0.5
=
截頭円柱
h
1
=
h
2
=
R=
V=πR
2
(h
1
+h
2
)/2
=
A
s
=πR(h
1
+h
2
)
=
D=[4R
2
+(h
2
-h
1
)
2
]
0.5
=
円垂
R=
l=
h=
V=πR
2
h/3
=
A
s
=πRl
=
l=(R
2
+h
2
)
0.5
=
x=h/4
=
截頭角垂
A
b
=
A
b1
=
a=
h=
V=h/3[A
b
+A
b1
+(A
b
A
b1
)
0.5
]
=
A
b
=3√3a
2
/2=2.598a
2
=
x=h/4*[A
b
+2(A
b
A
b1
)
0.5
+3A
b1
]/ [A
b
+(A
b
A
b1
)
0.5
+A
b1
]
=
截頭円垂
R=
r=
a=
b=
l=
h=
V=πh/3*(R
2
+Rr+r
2
)
=
V=h/4[πa
2
+πb
2
/3]
=
A
s
=πla=
a=R+r=
b=R-r=
l=(b
2
+h
2
)
0.5
=
x=h/4*(R
2
+2Rr+3r
2
)/(R
2
+Rr+r
2
)
=
方光体
a=
a
1
=
b=
b
1
=
h=
V=h/6*[(2a+a
1
)b+(2a
1
+a)b
1
]
=h/6[ab+(a+a
1
)(b+b
1
)+a
1
b
1
]
=
x=h/2*(ab+ab
1
+a
1
b+3a
1
b
1
)/(2ab +ab
1
+a
1
b+2a
1
b
1
)
=
角垂
a=
h=
A
b
=
V=A
b
h/3=
A
b
=3*3
0.5
a
2
/2
=2.598a
2
=
x=h/4=
円環
R=
r=
D=
d=
V=2π
2
Rr
2
=19.739Rr
2
=
V=π
2
Dd
2
/4=2.4674Dd
2
=
S=4π
2
Rr=39.478Rr
=
S=π
2
Dd=9.8696Dd
=
球
r=
d=
V=
V=4πr
3
/3=4.188790205r
3
=
V=πd
3
/6=0.523598776d
3
=
S=4πr
2
=
S=πd
2
=
r=(3V/4π)
1/3
=0.620351V
1/3
=
r=d/2=
球状の楔形
r=
h=
a=
V=2πr
2
h/3
=2.0943951024r
2
h
=
S=πr(2h+a)
=
x=3/8*(2r-h)
=
欠球
a=
h=
V=
r=
V=πh/6*(3a
2
+h
2
)
=
V=πh
2
/3*(3r-h)
=
A
s
=2πVh
=
A
s
=π(a
2
+h
2
)
=
a
2
=h(2r-h)=
x=3/4*(2r-h)
2
/(3r-h)
=
a=
b=
h=
r=
V=πh/6*(3a
2
+3b
2
+h
2
)
=
A
s
=2πrh
=
r
2
=a
2
+[(a
2
-b
2
-h
2
)/2h]
2
=
参考文献：「標準機械設計図表便覧 改新 増補４版」 （小栗冨士雄、小栗達男 共著） 数および数の計算 第1-3頁 立体の容積および諸数値を参考。