The curved surface area of a cone of slant height l and radius r is given by:

(1) 1/3 πr²

(2) πrl

(3) πrl²

(4) 1/3 πrl

The curved surface area of a cone is the measurement (perimeter) of the curved face. 

Answer: The Curved Surface Area of a cone is πrl.

Let's see how?

Explanation:

Given in the question that, the radius of the cone is r  and the slant height of the cone is l.

Since a cone looks like a square pyramid with a circular base and curved surface, its curved surface area, and lateral surface area are related.

The lateral surface area of a triangular face in a square pyramid is 1/ 2 a × l, where a is the altitude and l is the slant height of the square pyramid.

If we replace 'a' by '2πr'  as the cone has a curved face with a circular base then we get,

⇒ 1 / 2 (2πr) × l  

⇒ πrl 

Thus, the curved surface area of a cone is πrl (2)