Ans: (a) $75^\circ$ (b) $(5\pi + 24) \text{ cm}$
- Let $\theta$ be the angle of the sector.
$\begin{array}{rcl}
\pi (12)^2 \times \dfrac{\theta}{360^\circ} & = & 30 \pi \\
\theta & = & 75^\circ
\end{array}$Therefore, the angle of the sector is $75^\circ$.
- Hence, the perimeter of the sector
$\begin{array}{cl}
= & 2 \pi (12) \times \dfrac{75^\circ}{360^\circ} + 2 \times 12 \\
= & (5\pi + 24) \text{ cm}
\end{array}$
