S = { 0 ≤ ϕ ≤ 2 π ,   0 ≤ θ ≤ π ,   0 ≤ ρ ≤ R } V o l u m e = 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