Let the length of the generatrix of the cone be r, the radius of the base circle be r, and the central angle of the fan-shaped circle in the side development diagram be n.

Then the circumference of the cone bottom is: 2πr, which is the arc length of the sector in the side development diagram.

So the lateral area of the cone is: 1/2*2πr*R, or n/360*πR?

So 1/2*2πr*R= n/360*πR?

Solution: r=nR/360. ( 1)

The lateral area is twice that of the bottom.

That is, 1/2*2πr*R=2πr?

The solution is R=2r. (2)

(1)(2) At the same time, too

n= 180

Therefore, the fan-shaped central angle of the conical profile is 180.