Step 1 (i): For a parallel plate capacitor with dielectric constant $K$ filling the gap, plate area $A$, separation $d$: the field is reduced by factor $K$ due to polarization, giving $C = \dfrac{K\varepsilon_0A}{d}$.

Step 2 (ii): Potential at surface of a charged conducting sphere: $V = \dfrac{kQ}{R} = \dfrac{9\times10^9\times6\times10^{-6}}{0.2} = \dfrac{5.4\times10^4}{0.2} = 2.7\times10^5$ V.

Step 3: For a conductor, the entire sphere (including interior) is an equipotential region — so potential at the CENTRE equals potential at the SURFACE: $V_{centre}=2.7\times10^5$ V.