Proof of Formula for the Curved Surface Area of Cone
For the cone of slant height
and base radius
the curved surface area
is 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) where
is in radians.
The circumference of the base of the cone is equal to the arc length so
and
Substitute this into (1) to obtain