2012-II-16

Ans: B
Let $\angle AOB=\theta$.

Consider the sector $OAB$,

$\begin{array}{rcl}
2\pi (30) \times \dfrac{\theta}{360^\circ} & = & 12 \pi \\
\theta & = & 72^\circ
\end{array}$

Consider the sector $OCD$,

$\begin{array}{rcl}
2\pi (30+AC)\times \dfrac{72^\circ}{360^\circ} & = & 16 \pi \\
30 + AC & = & 40 \\
AC & = & 10 \mbox{ cm}
\end{array}$