The area of the base of a right circular cone is 154 cm² and its height is 14cm. Its curved surface area is

Given: Area of the base of a right circular cone is 154 cm².

Height of the cone is 14 cm.

Curved surface area of a cone is : πrl (here r and l are radius and slant height respectively)

Area of the base is given by: πr²

∴ π × r² = 154

⇒ r² = = 49

⇒ r = √49 = 7cm

∴ radius of the base of the cone is 7cm

Now,

l = √(r² + h²)

∴ πrl = πr√(r² + h²)

Let S be the CSA of the cone.

∴ S = πr√(r² + h²)

⇒ S = π × (7) × √((7)² + (14)²)

⇒ S = π × (7) × √(49 + 196) = π × (7) × √(245)

⇒ S = π × (7) × 7√5 = × 7 × 7√5 = 154√5

∴ S = 154√5 cm²

That is CSA of the cone is 154√5 cm²