#### Answer

d = 5.56* $10^{-3}$ mm

#### Work Step by Step

V = 90.0 * $10^{-12}$ $cm^{3}$
V of sphere = $\frac{4}{3} * π * r^{3}$
$\frac{4}{3} * π * r^{3}$ = 90.0 * $10^{-12}$
$π * r^{3}$ = $\frac{3}{4}$ * 90.0 * $10^{-12}$
$π * r^{3}$ = $6.75 * 10^{-11}$
$ r^{3}$ = $\frac{6.75 * 10^{-11}}{π}$
r = $\sqrt[3] \frac{6.75 * 10^{-11}}{π}$
r = 2.780041634 * $10^{-4}$ cm
d = 2 * r
d = 2 * 2.780041634 * $10^{-4}$ cm = 5.560083268 * $10^{-4}$ cm
d = 5.560083268 * $10^{-3}$ mm
Rounding to 3 significant figures gives d = 5.56* $10^{-3}$ mm