The volume of a right circular cone is $2464{\text{cm}}^3$. If the radius of its base is $14\text{cm}$, then its curved surface area (in ${\text{cm}}^2$) is: (Take $\pi =\frac{22}{7}$)

The volume of a right circular cone is given by:
$$V=\frac{1}{3}\pi r^{2}h$$
Given that $V=2464{\text{cm}}^3$ and $r=14\text{cm}$:
$$2464=\frac{1}{3}\times \frac{22}{7}\times 14\times 14\times h$$
$$2464=\frac{1}{3}\times 22\times 2\times 14\times h$$
$$2464=\frac{616}{3}\times h$$
$$h=\frac{2464\times 3}{616}=4\times 3=12\text{cm}$$
Now, find the slant height ($l$) of the cone:
$$l=\sqrt{r^2+h^2}$$
$$l=\sqrt{14^2+12^2}=\sqrt{196+144}=\sqrt{340}=\sqrt{4\times 85}=2\sqrt{85}\text{cm}$$
The curved surface area (CSA) of a cone is given by:
$$\text{CSA}=\pi rl$$
$$\text{CSA}=\frac{22}{7}\times 14\times 2\sqrt{85}=22\times 2\times 2\sqrt{85}=88\sqrt{85}{\text{cm}}^2$$