  In this paper, we focus on a conformally flat Riemannian manifold $(M^n,g)$
of dimension $n$ isometrically immersed into the $(n+1)$-dimensional light-cone
$\Lambda^{n+1}$ as a hypersurface. We compute the first and the second
variational formulas on the volume of such hypersurfaces. Such a hypersurface
$M^n$ is not only immersed in $\Lambda^{n+1}$ but also isometrically realized
as a hypersurface of a certain null hypersurface $N^{n+1}$ in the Minkowski
spacetime, which is different from $\Lambda^{n+1}$. Moreover, $M^n$ has a
volume-maximizing property in $N^{n+1}$.
