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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.

We see cross sections in everyday life.
bread3
A "slice" of bread.
Cross section: breadslice
cucumberA "slice" of cucumber. Cross section: cucumberslice
cuttree
A "slice" of log.
Cross section: cucumberslice


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

crossPoint

The plane is tangent to the sphere, intersecting in only one point.

Line Segment
crossSegment
The plane is tangent to the side of the cylinder, intersecting in a line segment.
Figure
crossFigure
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.
CScircle
Right circular cylinder
Cross section: CScylinder rectangle
Plane orientation: perpendicular to the bases

CSellipse

Right circular cone
Cross section: CSsquare ellipse
Plane orientation: slanted (angled) across the cone

CSprism


Right square prism
Cross section: CSsquare 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.

sword1

sword1a

sword2

sword2a
sword3

sword3a

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.


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