The net of a cone is a sector for the curved side, with the base circle attached to it. The radius of the sector is the slant height, and its arc is as long as the base circumference. The cone here has radius 1 and slant height 2, so the sector has radius 2 and an arc of length 2π.
The central angle of the sector is 2π times the base radius divided by the slant height. The arc is the base circumference 2πr and the radius is the slant height l, so the angle comes out as 2πr divided by l. A radius exactly half the slant gives 180 degrees, a semicircle. The longer the slant, the narrower the sector and the sharper the cone.
The side is curved, so it is cut into 48 thin wedges that fold a little at a time and roll around the apex. The base circle lifts about the line where it touches the arc. The angle between the side and the base is the angle the slant makes with the base, so with radius 1 and slant 2 the slant meets the base at 60 degrees and each crease closes through 120 degrees.