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