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If a circular cone is intersected by a plane only at its vertex what shape is produced?
When a circular cone is intersected by a plane at only its vertex, the resulting shape is a single point, which is the vertex itself. There are no other intersecting points along the surface of the cone. Thus, no additional geometric figure is formed beyond this singular point.
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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 as in the picture below what shape is produced?
When a right circular cone is intersected by a plane that passes through its vertex and touches the edge of each nappe, the resulting shape is a triangle. This triangle is formed by the intersection line extending from the vertex to the edges of the cone's surfaces, effectively creating a triangular cross-section of the cone.
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 intersects a plane that runs perpendicular to the cones axis (but does not pass through the vertex the resulting curve will be an?
The intersection of a right circular cone with a plane that is perpendicular to the cone's axis and does not pass through the vertex will result in a circle. This is because the plane cuts through the cone at a constant distance from the vertex, creating a cross-section that is a circle. The size of the circle depends on how far the plane is from the vertex along the cone's axis.
If a right circular cone intersects a plane that runs parallel to the cone's axis but does not pass through its vertex?
If a right circular cone intersects a plane that runs parallel to the cone's axis but does not pass through its vertex, the resulting curve is a pair of hyperboles.
What dimensional shapes have circular faces?
Not sure what the question means, unless it is meant to refer to 3-dimensional shapes. If so, some answers are: a cylinder, a cone, a section of a sphere, an ellipsoid with two equal axes intersected by a plane defined by those axes, a symmetric paraboloid intersected by a plane perpendicular to its axis of symmetry, a torus (doughnut) intersected by a plane perpendicular to its "main" radius.
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.
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 a right circular cone is intersected by a plane only at its vertex what figure it is?
A point.
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
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 so that the intersection goes through the cone's vertex as well as an edge of each nappe as in the picture below what shape is produced?
When a right circular cone is intersected by a plane that passes through its vertex and touches the edge of each nappe, the resulting shape is a triangle. This triangle is formed by the intersection line extending from the vertex to the edges of the cone's surfaces, effectively creating a triangular cross-section of the cone.
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.
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 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.
If a right circular cone is intersected by a plane that passes through only one nappe of the cone but is not parallel to an edge of the cone what shape is produced?
An ellipse is produced.
