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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 will be an?
hyperbola
Which solid figure has only one face?
cone +++ A sphere or other full solid of revolution generated about either axis where the curve meets that axis in 2 places, and those intercepts are the solid's poles. (A cone has 2 faces)
What figure is formed by the intersection of a cone?
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
If a right circular cone intersects a plane that runs perpendicular to the cones axis but does not pass through its vertex the resulting curve will be an?
circle
What is a cone in 2D?
It depends on your the inclinantion of the plane which is used to "slice" the cone. The answer can be a circle, ellipse, parabola, hyperbola or two intersecting lines. These (apart from the last) are known as conic sections. In terms of the 2-d figure that generates a cone, the answer is a straight line, with a non-zero slope, rotated about the x-axis.
