The apex of a cone is always the same distance, equal to the sant height, from the edge of the base. This means that when we cut the cone along a straight line from the base to the apex and unfold it, the shape formed is a sector of a circle.
The radius of the circle is equal to the slant height and the length of the arc of the sector is equal to the circumference of the base of the cone.
The angle subtended by the arc of the sector is
From the cone, using Pythagoras Theorem gives
so that