= Solution
Using a center-to-edge <sound-crossing time> $t_s=R/c_s$ and the pressureless uniform-sphere <free-fall time of a uniform sphere> $t_{\rm ff}=\sqrt{3\pi/(32G\rho)}$, equality gives
$$
\boxed{R_{\rm cross}=c_s\sqrt{\frac{3\pi}{32G\rho}}\sim\frac{c_s}{\sqrt{G\rho}}.}
$$
On scales larger than this estimate, <pressure> information cannot cross the region before its gravitational dynamical evolution. It therefore identifies the order of the <Jeans length> and separates gravity-dominated from pressure-supported behavior in the simple comparison. It is not an exact normal-mode stability calculation: with the standard Jeans <wavelength> $\lambda_J=c_s\sqrt{\pi/(G\rho)}$, this radius is $\sqrt{3/32}\lambda_J$. Using the diameter rather than the radius as the crossing distance changes the numerical coefficient. <Boundary conditions>, <density> structure, <turbulence> and magnetic support also matter for an actual cloud.
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