Mathematically, the line from the apex of the cone to any point on the circumference of the bottom of the cone is called the generatrix of the cone;

Cut along any generatrix of the cone and expand it into a plane figure, that is, a sector;

The radiu of that expanded sector is the generatrix of the cone,

The arc length of the expanded sector is the circumference of the cone bottom;

Through expansion, the side area of three-dimensional graphics is converted into the area of plane graphics.

Solution: Let the generatrix length of the cone be L and the radius of the bottom surface of the cone be R,

Then the fan-shaped radius is L, and the arc length is the circumference of the cone bottom (2πR).

We already know that the formula of sector area is: S = (1/2)× sector radius× sector arc length.

= ( 1/2)× L × (2πR)

= π R L

That is, the lateral area of the cone is π times the product of the radius of the cone bottom surface and the length of the cone generatrix.