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The most interesting intersections of cone are its planar sections (intersections with a plane). These sections are called "conic"
The figures can be
1) dot - for plane going through apex
2) two lines - for plane containing cone axis
3) one line - for plane going through apex and touching the cone
3) circle - for plane orthogonal to cone axis
4) ellipsis - for plane that intersects the cone axis and generating lines
5) parabola - for plane parallel to a generating line
4) hyperbola - other cases
See wikipedia's "conic section" article
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What shape is formed by the intersection of a cone and a plane that is parallel to a cone's base not containing the cone's vertex?
The shape described by the intersection of the cone and the plane is simply a circle.
What type of geometric figure is formed by the intersection of two lines?
it is the difference of the edges that contract the same sides. so the answer is line point
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 what shape is produced?
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.
What is a 3d cone called?
The cone IS a 3d figure.
The figure formed by the intersection of a solid with a plane parallel to the base of the solid is congruent to the base if the solid is a?
The answer would be a right cylinder. A right cylinder is a cylinder that has a closed circular surface having two parallel bases on both the ends and whose elements are perpendicular to its base.
