Ans: C
Note that the area of the shaded region is the difference of the area of the sector $OCD$ and that of the sector $OAB$. Hence, we have
Note that the area of the shaded region is the difference of the area of the sector $OCD$ and that of the sector $OAB$. Hence, we have
$\begin{array}{rcl}
\pi \times (OA+6)^2 \times \dfrac{60^\circ}{360^\circ} – \pi \times (OA)^2 \times \dfrac{60^\circ}{360^\circ} & = & 54\pi \\
\dfrac{\pi}{6}[(OA)^2 +12OA +36 – (OA)^2 ] & = & 54 \pi \\
12OA +36 & = & 324 \\
12OA & = & 288 \\
OA & = & 24
\end{array}$
