The right circular cone of height 24 cm has a volume of 1232 cm³, then the area of its curved surface is?

Question: The right circular cone of height 24 cm has a volume of 1232 cm³, then the area of its curved surface is?

Solution:
Volume of the cone = (1/3) × r² × h = 1232
⇒ (1/3) × (22/7) × r² × 24 = 1232
⇒ r² = (1232 × 7 × 3)/(22 × 24)
⇒ r² = 49
∴ r = 7

So, slant height l = √(7)² + (24)² = √625 = 25
So, curved surface area = πrl = (22/7) × 7 × 25 = 550 cm³