Surface Integrals, Stokes & Divergence · Easy problem

The cone $z = \sqrt{x^2 + y^2}$, $0 \le z \le 2$, is parametrized by $\mathbf r(u, v) = (u\cos v, u\sin v, u)$ with $0 \le u \le 2$, $0 \le v \le 2\pi$. Find its surface area $\iint_S dS$. Give an exact answer.