Solution
Let the radius of the sphere be $r \mathrm{~cm}$.
Then, its volume $=\left(\frac{4}{3} \pi r^{3}\right) \mathrm{cm}^{3}$.
$$
\begin{aligned}
\therefore \quad \frac{4}{3} \pi r^{3}=4851 & \Rightarrow \frac{4}{3} \times \frac{22}{7} \times r^{3}=4851 \\
& \Rightarrow r^{3}=\left(4851 \times \frac{3}{4} \times \frac{7}{22}\right)=\left(\frac{441 \times 21}{8}\right)=\left(\frac{21}{2}\right)^{3} \\
& \Rightarrow r=\frac{21}{2}=10.5 .
\end{aligned}
$$
Thus, the radius of the sphere is $10.5 \mathrm{~cm}$.
Surface area of the sphere $=\left(4 \pi r^{2}\right)$ sq units
$$
\begin{aligned}
&=\left(4 \times \frac{22}{7} \times \frac{21}{2} \times \frac{21}{2}\right) \mathrm{cm}^{2} \\
&=1386 \mathrm{~cm}^{2} .
\end{aligned}
$$
Hence, the surface area of the given sphere is $1386 \mathrm{~cm}^{2}$.