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If both nappes of a right circular cone are intersected by a plane that does not pass through the vertex of the cone the resulting curve will be a?
It will be a hyperbola.
What shape is produced if a right circular cone is intersected by a plane that goes through both nappes of the cone but not through the vertex?
An Ellipse
If both nappes of a right circular cone are intersected by a plane that does not pass through the vertex of the cone the resulting curve will be a(n) .?
hyperbola
Which two-dimensional figure could be a cross section of a rectangular pyramid that has been intersected by a plane perpendicular to its base and not through its vertex?
trapezoid
If a right circular cone is intersected by a plane only at its vertex as in the picture below what shape is produced?
The answer will depend on the angle formed between the plane and the axis of the cone. Since there is no picture "below" it is not possible to determine that and therefore it is impossible to give an answer.
If a right circular cone is intersected by a plane only at its vertex what shape is produced?
The intersection will consist of only one point.
If both nappes of a right circular cone are intersected by a plane that does not pass through the vertex of the cone the resulting curve will be a?
It will be a hyperbola.
What shape is produced if a right circular cone is intersected by a plane that goes through both nappes of the cone but not through the vertex?
An Ellipse
If both nappes of a right circular cone are intersected by a plane that does not pass through the vertex of the cone the resulting curve will be a(n)?
hyperbola
If both nappes of a right circular cone are intersected by a plane that does not pass through the vertex of the cone the resulting curve will be a(n) .?
hyperbola
If a circular cone is intersected by a plane so that the intersection goes through its vertex as well as the edge of the nappe what shape is produced?
If I understand your description correctly, a line.
If a right circular cone is intersected by a plane that goes through both nappes of the cone but not through the vertex as in the picture below what shape is produced?
A line is produced
Which two-dimensional figure could be a cross section of a rectangular pyramid that has been intersected by a plane perpendicular to its base and not through its vertex?
trapezoid
What geometric shape has 1 circular base?
A sphere intersected by a plane, An circular ellipsoid intersected by a plane, A cylinder, A cone, and many more shapes, some of which don't even have a name!
If a right circular cone is intersected by a plane only at its vertex as in the picture below what shape is produced?
The answer will depend on the angle formed between the plane and the axis of the cone. Since there is no picture "below" it is not possible to determine that and therefore it is impossible to give an answer.
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 has a circular base and a vertex that isn't in the same plane as the base?
A shape with a circular base and a vertex that isn't in the same plane as the base is called a cone.
