  The well known Weyl's asymptotic formula gives an approximation to the number
$\mathcal{N}_{\omega}$ of eigenvalues (counted with multiplicities) on an
interval $[0,\>\omega]$ of the Laplace-Beltrami operator on a compact
Riemannian manifold ${\bf M}$. In this paper we approach this question from the
point of view of Shannon-type sampling on compact Riemannian manifolds. Namely,
we give a direct proof that $\mathcal{N}_{\omega}$ is comparable to cardinality
of certain sampling sets for the subspace of $\omega$-bandlimited functions on
${\bf M}$.
