The apex angle of the cone is the angle that the apex takes. This is measured by the two intersections the cone takes through a perpendicular plane defined by the apex and the center of the circular base.
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If a right circular cone is intersected by a plane so that the intersection goes through the cone's vertex as well as an edge of each nappe, the shape produced is a line. Not asked, but... If the angle of the plane is less than the angle of the cone, then the intersection is a point. If the angle of the plane is greater than the angle of the cone, then the intersection is two lines intersecting at the vertex. If the plane insersects at other than the vertex, then the intersection is a circle when the plane is perpendicular to the cone's axis, an ellipse when the plane's angle is less than the cone's angle, a parabola when the planes's angle equals the cone's angle, and two hyperbole's in the last case.
the cone has three sides
there are 2 Faces on a cone, there is a technically immeasurable amount of corners, because the ca just keep cutting the angle finer and finer on the circular end and making more corners. though you'll get your bottom whipped if you say this to your teacher, the amount of vertexes on a cone is: 1+(∞)
The interception of a plane with a cone parallel to the base of the cone is a circle.
A cone has two faces.