Consider a smooth $2$-dimensional closed Riemannian manifold $M$ and $x \in M$. Let $ 0 < r< \text{inj}(M) $ and let $\mathcal{H}^1$ be the Hausdorff measure induced by the Riemannian distance. Where can I find a proof of the fact that there exists a positive constant $C$ s.t. $$ \mathcal{H}^1(\partial B(x,r)) \le Cr $$ ?
Thank you.