= Solution
Use the <amphiphile packing parameter> $P=v/(a_0\ell_c)$, where $v$ is tail <volume>, $a_0$ the effective head-group <area> and $\ell_c$ the maximum tail extension. The conventional cylindrical-<micelle> window is $1/3\lesssim P\lesssim1/2$. Its upper limit follows directly from <cylindrical micelle geometry>: a long core of radius $R$ has volume-to-area ratio $R/2$, so $v/a_0=R/2\leq\ell_c/2$. The spherical packing limit is $P=1/3$; above it a filled spherical core cannot accommodate the assumed head-group <area> and chain length.
Inverting both positive inequalities gives
$$
\frac{2v}{\ell_c}\lesssim a_0\lesssim\frac{3v}{\ell_c},\qquad
\boxed{0.246\,\mathrm{nm^2}\lesssim a_0\lesssim0.369\,\mathrm{nm^2}.}
$$
Thus the useful estimate is \b[a head-group area of approximately $0.25$–$0.37\,\mathrm{nm^2}$]. If phase-boundary configurations are excluded, use strict inequalities. These endpoints are geometric morphology crossovers, rather than exact thermodynamic phase boundaries: chain conformations and head-group interactions also affect which <micelle> minimizes the <free energy>. The supplied molecular <volume> is interpreted as the tail-core <volume> required by this packing model.<Theory of self-assembly of hydrocarbon amphiphiles by Jacob N. Israelachvili and others>[1976, aggregate packing theory; cylindrical and spherical core constraints]{ref}
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