 Cross Sections MathBitsNotebook.com Terms of Use   Contact Person: Donna Roberts   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.

We see cross sections in everyday life. A "slice" of bread. Cross section:  A "slice" of cucumber. Cross section:  A "slice" of log. Cross section: 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. 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.

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.      The maximum number of "sides" of a cross section equals the number of faces (surfaces) of the solid. Since the rectangular prism shown above has 6 faces, a cross section of that solid may have at most 6 sides. So a hexagon (6 sided) cross section is possible, but an octagon (8 sided) cross section is not possible. 