How much metal sheet will be required to make a cone of height 4 m and base radius 3m? (π = 3.14)

We have

Given: radius of base of cone, r = 3 m

Height of the cone, h = 4 m

So, in right-angled ∆BOC, by using Pythagoras theorem,

BC² = OB² + OC²

⇒ BC² = r² + h²

⇒ BC² = 3² + 4²

⇒ BC² = 9 + 16 = 25

⇒ BC = √25 = 5

⇒ l = 5 m

Slant height of cone = 5 m

Metal required to make cone will cover the curved surface of the cone. So, curved surface area of the cone is given by

CSA = πrl

⇒ CSA = 3.14 × 3 × 5

⇒ CSA = 47.1

Thus, curved surface area is 47.1 m².