#### Answer

$V = 4.2 \times 10^{-12}~cm^3$
$A = 1.3 \times 10^{-5}~mm^2$

#### Work Step by Step

The radius is half the diameter, so the radius $r$ is $1.0 ~\mu m$
We can convert the radius to units of cm.
$r = (1.0 ~\mu m)(\frac{10^{-4} ~cm}{1 ~\mu m}) = 1.0 \times 10^{-4} ~cm$
We can use the radius to find the volume.
$V = \frac{4}{3}\pi ~r^3 = \frac{4}{3}\pi ~(1.0 \times 10^{-4} ~cm)^3$
$V = 4.2 \times 10^{-12}~cm^3$
We can convert the radius to units of mm.
$r = (1.0 ~\mu m)(\frac{10^{-3} ~mm}{1 ~\mu m}) = 1.0 \times 10^{-3} ~mm$
We can use the radius to find the surface area.
$A = 4\pi ~r^2 = 4 \pi ~(1.0 \times 10^{-3} ~mm)^2$
$A = 1.3 \times 10^{-5}~mm^2$