Cross-section per unit mass
= Cross-section per unit mass
For an equal-density sphere of diameter $D$, the ratio of geometric cross-section to mass is
$$
\frac{\pi D^2/4}{\pi\rho D^3/6}=\frac{3}{2\rho D}.
$$
Breaking a fixed mass into smaller pieces therefore increases its total cross-section in inverse proportion to fragment size.