The volume of a right circular cone is 1232 cm³ and its vertical height is 24 cm. Its curved surface area is

$$\eqalign{ & {\text{Volume of a cone}} = \frac{1}{3}\pi {r^2}h \cr & \frac{1}{3}\pi {r^2}\left( {24} \right) = 1232{\text{ c}}{{\text{m}}^2} \cr & {r^2} = \frac{{1232 \times 3 \times 7}}{{24 \times 22}} \cr & {r^2} = 7 \times 7 \cr & r = \sqrt {7 \times 7} \cr & r = 7{\text{ cm}} \cr & l = \sqrt {{r^2} + {h^2}} \cr & = \sqrt {{7^2} + {{24}^2}} \cr & = \sqrt {625} \cr & = 25 \cr & {\text{Curved surface area}} = \pi rl \cr & = \frac{{22}}{7} \times 7 \times 25 \cr & = 550{\text{ c}}{{\text{m}}^2} \cr} $$