Answer
$2.5\times 10^{-4}m$
Work Step by Step
Assuming that the total volume of a typical human lung is 2.4 liters $(0.0024m^3)$ and that the alveoli are perfect spheres, we can find the diameter of an alveolus from the volume of a sphere, $\frac{4}{3}\pi r^{3}$
$$\frac{4}{3}\pi r^{3}=\frac{4}{3}\pi (\frac{d}{2})^{3}=\frac{\pi d}{6}=1 alveolus$$
$$(3\times 10^{8})\frac{\pi d}{6}=0.0024m^3$$
$$d=\sqrt[3] (\frac{6(0.0024m^3)}{3\times 10^{8} \pi})$$
$$d=2.5\times 10^{-4}m$$
