Answer
The diameter is 0.20 mm.
Work Step by Step
We can use the volume of one alveolus to find the radius.
$V = 4.2 \times 10^6 ~\mu m^3$
$\frac{4}{3}\pi r^3 = 4.2 \times 10^6 ~\mu m^3$
$r^3 = \frac{(3)(4.2 \times 10^6 ~\mu m^3)}{(4 \pi)}$
$r^3 = 1.003 \times 10^6 \mu m^3$
$r = 1.0 \times 10^2 \mu m$
We can convert this radius to units of mm.
$r = (1.0 \times 10^2 \mu m)(10^{-3} ~mm/\mu m)$
$r = 0.10 ~mm$
The diameter is 2r which is 0.20 mm.
