Solution:

Area bounded by the curve, $y^{2}=4 x, y$-axis, and $y=3$ is represented as

$\begin{aligned}
\therefore \text { Area } \mathrm{OAB} &=\int_{0}^{3} x d y \\
&=\int_{0}^{3} \frac{y^{2}}{4} d y \\
&=\frac{1}{4}\left[\frac{y^{3}}{3}\right]_{0}^{3} \\
&=\frac{1}{12}(27) \\
&=\frac{9}{4} \text { units }
\end{aligned}$
As a result, the correct answer is $B .$