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
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