= Solution
Normalize $a_0=1$ and use the open dust model, with no <cosmological constant> and negligible present radiation. The <Friedmann equation> at the present epoch reads $H_0^2=H_0^2\Omega_m-kc^2$. Since $k=-r_{\rm curv}^{-2}$, the <curvature radius of an open FLRW universe> is
$$
\boxed{r_{\rm curv}=\frac{c}{H_0\sqrt{1-\Omega_m}}.}
$$
In the metric's $c=1$ convention the numerator is one. With $a_0=1$ this is also the present physical curvature radius; at <scale factor> $a$ the physical radius is $a r_{\rm curv}$. Inferring curvature from $\Omega_m$ alone would require this matter-only assumption; an additional dark-energy density would also enter the present <Friedmann equation>.
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