  Let $R$ be a commutative noetherian local ring and denote by
$\operatorname{mod} R$ the category of finitely generated $R$-modules. In this
paper, we give some evaluations of the singular locus of $R$ and annihilators
of Tor and Ext from a viewpoint of the finiteness of dimensions/radii of full
subcategories of $\operatorname{mod} R$. As an application, we recover a
theorem of Dey and Takahashi when $R$ is Cohen--Macaulay. Moreover, we obtain
the divergence of the dimensions of specific full subcategories of
$\operatorname{mod} R$ in non-Cohen--Macaulay case.
