Surface Integrals, Stokes & Divergence · Hard problem

A conical tent's fabric is the lateral surface $z = \sqrt{x^2+y^2}$ for $0\le z\le 4$ (apex on the ground, opening to radius $4$ m at the top). To resist ice buildup, the fabric's area density increases with height: $\delta(x,y,z) = z$ kg/m$^2$. Using the parametrization $\mathbf r(u,v) = (u\cos v, u\sin v, u)$, find the total mass of the fabric, in kilograms.