= Solution
Overlap means roughly one coil per coil <volume>. With segment <volume> $a^3$, the corresponding <polymer overlap volume fraction> is
$$
\phi^*\sim\frac{Na^3}{R_g^3}.
$$
For a strong <good solvent>, $R_g\sim aN^{3/5}$, and hence
$$
\boxed{\phi^*\sim N^{-4/5}=(10^4)^{-4/5}\simeq6.3\times10^{-4},}
$$
or about \b[0.063% by <volume>] in the unit-prefactor scaling convention. The segment <length> cancels. A coil has no sharply defined boundary, so using $4\pi R_g^3/3$ or retaining a size amplitude changes an order-one prefactor. This calculation is a scaling estimate, not an exact volume-fraction measurement.
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