Answer
$\frac{C}{A} = 6.79\times 10^{-4}~F/m^2$
Work Step by Step
Note that the number of electrons is the volume multiplied by the electron density.
That is, the number of electrons is: $~~A~d~(8.49\times 10^{28})$
We can find $\frac{C}{A}$:
$CV = q$
$CV = A~d~(8.49\times 10^{28}~m^{-3})(1.6\times 10^{-19}~C)$
$\frac{C}{A} = \frac{d~(8.49\times 10^{28}~m^{-3})(1.6\times 10^{-19}~C)}{V}$
$\frac{C}{A} = \frac{(1.00\times 10^{-12}~m)~(8.49\times 10^{28}~m^{-3})(1.6\times 10^{-19}~C)}{20.0~V}$
$\frac{C}{A} = 6.79\times 10^{-4}~F/m^2$
