A torus of radius 2 (and cross-sectional radius 1) can be represented parametrically by the function r:D→R3

r(θ,ϕ)=<(2+cosϕ)cosθ,(2+cosϕ)sinθ,sinϕ)>

where D is the rectangle given by 0≤θ≤2π, 0≤ϕ≤2π
The surface area of the torus is