A right circular cone of vertical height 24 cm has volume  $1232{\text{cm}}^{\text{3}}$  . Its curved surface area is

$v=1232{\text{cm}}^3$

$\Rightarrow \frac{1}{3}\pi r^{2}h=1232$

$\Rightarrow \frac{1}{3}.\frac{22}{7}.r^2.24=1232$

$\Rightarrow r^2=1232.\frac{3}{1}.\frac{7}{12}.\frac{1}{24}$

$\Rightarrow r^2=49$

$\Rightarrow r=7\text{ cm}$

$\therefore C.S.A=\pi rl$

$=\frac{22}{7}\mathrm{.7.25}$

$=550{\text{cm}}^2$

$\left[\therefore l=\sqrt{r^2+h^2}=25\text{ cm}\right]$