If one intends to build a 1.0 farad capacitor using circular discs...

The capacitance of a parallel plate capacitor is given by $C = \dfrac{\varepsilon_0 A}{d}$.

For circular discs of radius $r$, the area is $A = \pi r^2$.

Substituting the area into the capacitance formula gives $C = \dfrac{\varepsilon_0 \pi r^2}{d}$.

Rearranging for $r^2$, we get $r^2 = \dfrac{C d}{\pi \varepsilon_0}$.

We know that $\dfrac{1}{4 \pi \varepsilon_0} = 9 \times 10^9 \Rightarrow \dfrac{1}{\pi \varepsilon_0} = 36 \times 10^9$.

Substituting the given values $C = 1.0\text{ F}$ and $d = 1.0\text{ mm} = 10^{-3}\text{ m}$:

$r^2 = 1.0 \times 10^{-3} \times 36 \times 10^9 = 36 \times 10^6\text{ m}^2$

$r = \sqrt{36 \times 10^6} = 6000\text{ m} = 6\text{ km}$