  For a domain $D \subset \mathbb C^n$, $n \ge 2$, let
$F^k_D(z)=K_D(z)\lambda\big(I^k_D(z)\big)$, where $K_D(z)$ is the Bergman
kernel of $D$ along the diagonal and $\lambda\big(I^k_D(z)\big)$ is the
Lebesgue measure of the Kobayashi indicatrix at the point $z$. This
biholomorphic invariant was introduced by B\locki and in this note, we study
its limiting boundary behaviour on two classes of domains namely,
$h$-extendible and strongly pseudoconvex polyhedral domains.
