Sector area: s = n π a 2/360

Area of circle: s = π r 2

The lateral area of the cone: S=πra(n is the central angle and a is the generatrix).

process

Solution: Because the cone lateral area = 2 times the area of the base circle.

So π ra = 2 π r 2

a=2r

And because the fan-shaped area spread on the side of the cone = twice the circular area of the bottom surface.

So n π a 2/360 = 2 π r 2

That is, n π (2r) 2/360 = 2 π r 2.

4nπr^2/360=2πr^2

n=2πr^2/(4πr^2/360)

n= 180

Therefore, the degree of the central angle of the conical profile is 180 degrees.