The volume of a sphere is 4851 cm3.

Let the radius of the sphere be $r$.

As,

Volume of the sphere $=4851 \mathrm{~cm}^{3}$

$\Rightarrow \frac{4}{3} \pi r^{3}=4851$

$\Rightarrow \frac{4}{3} \times \frac{22}{7} \times r^{3}=4851$

$\Rightarrow r^{3}=4851 \times \frac{3 \times 7}{4 \times 22}$

$\Rightarrow r^{3}=\frac{9261}{8}$

$\Rightarrow r=\sqrt[3]{\frac{9261}{8}}$

$\Rightarrow r=\frac{21}{2} \mathrm{~cm}$

Now,

Curved surface area of the sphere $=4 \pi r^{2}$

$=4 \times \frac{22}{7} \times \frac{21}{2} \times \frac{21}{2}$

$=1386 \mathrm{~cm}^{2}$

So, the curved surface area of the sphere is 1386 cm2.