derivation of curved surface area of cone
If a perpendicular cut is made from a point on the circumference of the base to the vertex and the cone is opened up, a sector of a circle with radius l is produced. Since the circumference of the base of the cone is 2πr, therefore the arc length of the sector of the circle is 2πr.
Now, curved surface area = Area of sector OAA’
Curved surface area = (Arc length of sector)/(Circumference of circle) x Area of circle
= (2πr/2πl) x πl^2
Hence, curved surface area of cone is πrl