S
=
{
0
≤
ϕ
≤
2
π
,
0
≤
θ
≤
π
,
0
≤
ρ
≤
R
}
Volume
=
∭
S
ρ
2
sin
θ
d
ρ
d
θ
d
ϕ
=
∫
0
2
π
d
ϕ
∫
0
π
sin
θ
d
θ
∫
0
R
ρ
2
d
ρ
=
ϕ
∣
0
2
π
(
−
cos
θ
)
∣
0
π
1
3
ρ
3
∣
0
R
=
2
π
×
2
×
1
3
R
3
=
4
3
π
R
3