= Solution
For a spherical <micelle> with $N$ tails, core radius $r$, molecular tail <volume> $v$ and head-group <area> $a$, volume and surface counting give $Nv=4\pi r^3/3$ and $Na=4\pi r^2$. Consequently $a=3v/r$. A tail cannot span a core radius larger than its maximum length $\ell$, so the <amphiphile packing parameter> condition is
$$
\boxed{a\geq\frac{3v}{\ell}=0.380\ \mathrm{nm^2}.}
$$
\b[This is a minimum area, not a maximum.] The printed request reverses the geometric inequality. The limiting value corresponds to fully extended tails with $r=\ell$; larger head groups permit smaller spherical aggregates in this simple packing argument. The supplied data alone impose no finite maximum head-group area, and geometry alone does not guarantee thermodynamic <micelle> formation.
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