Let $(X,d)$ be an $n (\geq2)$ dim Alexandrov space with curvature $\geq k$. $B(x,r)$ is an open ball in $X$. Let $M_{k,n}$ be the $n$ dim space form of constant curvature $k$. $B_k(r)$ is an open ball with radius $r$ in $M_{k,n}$.

Question: It is true that $H^{n-1}(\partial B(x,r)) \leq H^{n-1}(\partial B_k(r)) $? Here $H^{n-1}$ means the $(n-1)$ dim Hausdroff volume.