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Circle: If the knife is perpendicular to the axis of the cone.

Ellipse: If the knife is between (perpendicular to the axis of the cone) and (parallel to the side of the cone).

Parabola: If the knife is between (parallel to the side of the cone) and (parallel to the axis of the cone).

Hyperbola: If the knife is parallel to the axis of the cone.

Triangle: If the knife is perpendicular to the base of the cone.

Point: If the knife is parallel to the base the cone and through the apex

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Q: What is a cross section of a cone?

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The answer depends on the angle at which the axis of the cone intersects the cross-sections.

cone

Depends on the way you cut the cone, but the outline is either an ellipse or a parabola.

cone

No because it would be smaller.

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The vertical cross section of a right vertical cone is a triangle if that cross section is taken from the vertex. Any other vertical cross section will reveal a hyperbola (with endpoints on the base of the cone). A link can be found below.

Circle

The answer depends on the angle at which the axis of the cone intersects the cross-sections.

Circle

If it a right cone then it is a circle, otherwise an ellipse.

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A circular cross-section.

Circular when looking up at it

cone

By definition, the circular cross-section of a cone changes linearly in width as you go along its axis. By definition, the cross-section of a prism is constant along its axis. So, by definition, a cone prism is an impossible shape.

Depends on the way you cut the cone, but the outline is either an ellipse or a parabola.

For a right cone, it is a hyperbola which becomes and isosceles triangle when the section passes through the apex.

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