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Let $B(p,\epsilon )$ be an embedded normal ball in a Riemannian surface, with $0<\epsilon <\mathrm{inj}(p)$, and suppose its Gaussian curvature satisfies $K\le 0$. In geodesic polar coordinates, the area element of a surface is $h(r,\theta )drd\theta$, where the Jacobi equation in geodesic polar coordinates givesThus $h_r\ge 1$ and $h\ge r$. Integration provesThe embedded polar-coordinate range matters: a flat torus has zero Gaussian curvature, but sufficiently large metric balls cover the whole finite-area surface and cannot satisfy this bound for all radii. On a complete simply connected surface with $K\le 0$, the Cartan-Hadamard theorem removes that obstruction.