a
The expression for capacitance is given by,

\(C=\frac{A \varepsilon_{0} \varepsilon_{r}}{d}\) \(......(I)\)

Substitute \(15 \times 10^{-9}\) for \(C, 8.85 \times 10^{-12}\) for \(\varepsilon_{0}\) and \(2.5\) for \(\varepsilon,\) in equation \((I).\)

\(15 \times 10^{-9}=\frac{A\left(8.85 \times 10^{-12}\right)(2.5)}{d} \quad \ldots \ldots\) \((II)\)

The expression for electric field in given by,

\(E=\frac{V}{d}\)

\(30 \times 10^{6}=\frac{30}{d}\)

\(d=10^{-6} m\)

Substitute \(10^{-6} m\) for \(d\) in equation \(( II )\).

\(15 \times 10^{-9}=\frac{A\left(8.85 \times 10^{-12}\right)(2.5)}{10^{-6}}\)

\(A=\frac{15 \times 10^{-9} \times 10^{-6}}{8.85 \times 10^{-12} \times 2.5}\)

\(=6.7 \times 10^{-4} m ^{2}\)