= Solution
At $T=100\,\mathrm K$ with $\mu=2.3$, $c_s=\sqrt{k_BT/(\mu m_p)}\simeq599\,\mathrm{m\,s^{-1}}$. A solar-mass <Keplerian disk> has $v_K\simeq29.8\,\mathrm{km\,s^{-1}}$ at $1\,\mathrm{AU}$, so $\boxed{h/r\simeq0.020}$: the thin-disk approximation is consistent.
For fixed central <mass>, $h/r\propto T^{1/2}r^{1/2}$. If $T\propto r^{-q}$, then
$$
\boxed{h/r\propto r^{(1-q)/2},\qquad\text{flaring requires }q<1.}
$$
A flared outer disk intercepts more stellar radiation than a flat or self-shadowed disk, affecting its <temperature>, chemistry, vertical structure and observed <spectral energy distribution>. Heating changes the <sound speed> and therefore transport and dispersal; it can also enhance irradiation-driven mass loss. The actual coupled evolution depends on optical properties and transport, so flaring alone does not fix a unique lifetime. “Mid-planet” in the source is read as mid-plane.
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