Proof of Formula for the Curved Surface Area of Cone

For the cone of slant heightand base radiusthe curved surface areais give by the equation

To prove this equation, draw the net of the cone.

The net of the cone is a sector of a circle, with radiusand arc length equal to

The area of the sector is(1) whereis in radians.

The circumference of the base of the cone is equal to the arc length soandSubstitute this into (1) to obtain