The volume of a hemisphere is

As, volume of hemisphere $=2425 \frac{1}{2} \mathrm{~cm}^{3}$

$\Rightarrow \frac{2}{3} \pi r^{3}=2425 \frac{1}{2}$

$\Rightarrow \frac{2}{3} \times \frac{22}{7} \times r^{3}=\frac{4851}{2}$

$\Rightarrow r^{3}=\frac{4851 \times 3 \times 7}{2 \times 2 \times 22}$

$\Rightarrow r^{3}=\frac{441 \times 3 \times 7}{2 \times 2 \times 2}$

$\Rightarrow r^{3}=\frac{21^{3}}{2^{3}}$

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

So, the curved surface area of the hemisphere $=2 \pi r^{2}$

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

$=693 \mathrm{~cm}^{2}$