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Fropuff/Tables/Sphere volumes
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Tables
Dim
Area
Volume
1
2
{\displaystyle 2}
2
r
{\displaystyle 2r}
2
τ
r
{\displaystyle \tau \,r}
1
2
τ
r
2
{\displaystyle {\frac {1}{2}}\tau \,r^{2}}
3
2
τ
r
2
{\displaystyle 2\tau \,r^{2}}
2
3
τ
r
3
{\displaystyle {\frac {2}{3}}\tau \,r^{3}}
4
1
2
τ
2
r
3
{\displaystyle {\frac {1}{2}}\tau ^{2}r^{3}}
1
8
τ
2
r
4
{\displaystyle {\frac {1}{8}}\tau ^{2}r^{4}}
5
2
3
τ
2
r
4
{\displaystyle {\frac {2}{3}}\tau ^{2}r^{4}}
2
15
τ
2
r
5
{\displaystyle {\frac {2}{15}}\tau ^{2}r^{5}}
6
1
8
τ
3
r
5
{\displaystyle {\frac {1}{8}}\tau ^{3}r^{5}}
1
48
τ
3
r
6
{\displaystyle {\frac {1}{48}}\tau ^{3}r^{6}}
7
2
15
τ
3
r
6
{\displaystyle {\frac {2}{15}}\tau ^{3}r^{6}}
2
105
τ
3
r
7
{\displaystyle {\frac {2}{105}}\tau ^{3}r^{7}}
8
1
48
τ
4
r
7
{\displaystyle {\frac {1}{48}}\tau ^{4}r^{7}}
1
384
τ
4
r
8
{\displaystyle {\frac {1}{384}}\tau ^{4}r^{8}}
2
n
{\displaystyle 2n}
τ
n
(
2
n
−
2
)
!
!
r
2
n
−
1
{\displaystyle {\frac {\tau ^{n}}{(2n-2)!!}}r^{2n-1}}
τ
n
(
2
n
)
!
!
r
2
n
{\displaystyle {\frac {\tau ^{n}}{(2n)!!}}r^{2n}}
2
n
+
1
{\displaystyle 2n+1}
2
τ
n
(
2
n
−
1
)
!
!
r
2
n
{\displaystyle {\frac {2\tau ^{n}}{(2n-1)!!}}r^{2n}}
2
τ
n
(
2
n
+
1
)
!
!
r
2
n
+
1
{\displaystyle {\frac {2\tau ^{n}}{(2n+1)!!}}r^{2n+1}}
m
{\displaystyle m}
?
r
m
−
1
{\displaystyle ?r^{m-1}}
(
4
τ
)
1
−
(
−
1
)
m
4
τ
m
/
2
m
!
!
r
m
{\displaystyle \left({\frac {4}{\tau }}\right)^{\frac {1-(-1)^{m}}{4}}{\frac {\tau ^{m/2}}{m!!}}r^{m}}
m
{\displaystyle m}
?
r
m
−
1
{\displaystyle ?r^{m-1}}
(
τ
2
)
m
/
2
Γ
(
m
2
+
1
)
r
m
{\displaystyle {\frac {\left({\frac {\tau }{2}}\right)^{m/2}}{\Gamma \left({\frac {m}{2}}+1\right)}}r^{m}}