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A cross section is the intersection of a figure in three-dimensional space with a plane. A cross section is the face you obtain by making a "slice" through a solid object. A cross section is two-dimensional. |
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We see cross sections in everyday life.
A "slice" of bread.
Cross section: 
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 A "slice" of cucumber.
Cross section: 
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A "slice" of log.
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When a plane intersects a solid figure, the cross sectional face may be a point, a line segment, or a two-dimensional shape such as, but not limited to, a circle, rectangle, oval, or hexagon.
Point
The plane is tangent to the sphere, intersecting in only one point.
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Line Segment
The plane is tangent to the side of the cylinder, intersecting in a line segment. |
Figure
The plane cuts through the figure, intersecting in a pentagon. The plane may, or may not, be parallel to the base of the figure.
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The figure (face) obtained from a cross section depends upon
the orientation (angle) of the plane doing the cutting.
Right circular cylinder
Cross section:  rectangle
Plane orientation: perpendicular to the bases |
Right circular cone
Cross section:  ellipse
Plane orientation: slanted (angled) across the cone |
Right square prism
Cross section:
 square
Plane orientation: parallel to the bases of the prism |
A single solid figure can be sliced to produce numerous cross sections of different forms.
In the diagrams below, the sword represents the "slicing" plane.
The solid object is a right rectangular prism.
