2. A cylindrical bucket with a base diameter of $32 \mathrm{~cm}$ is filled with an appropriate amount of water. After placing an iron ball into the water, the ball is completely submerged, and the water level rises by $9 \mathrm{~cm}$ (no water spills out). The surface area of the ball is $\qquad$ $\mathrm{cm}^{2}$.
$$
2.576 \pi \mathrm{cm}^{2} \text {. }
$$

Let the radius of the sphere be $R$. According to the problem, we have
$$
\begin{array}{l}
\frac{4}{3} \pi R^{3}=\pi \cdot 16^{2} \times 9 \\
\therefore R=12 \\
\quad S=4 \pi R^{2}=4 \pi \cdot 12^{2}=576 \pi\left(\mathrm{cm}^{2}\right)
\end{array}
$$