Cross Sections - Math Is Fun

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Cross Sections

A cross section is the shape we get when cutting straight through an object.

cross section of prism The cross section of this prism is a triangle

It's like viewing the inside of something by cutting through it.

cross-section of a piece of celery A cross section of a piece of celery. Sliced loaf of bread

Example: Sliced Loaf of Bread

When we slice a loaf of bread, each slice forms a cross section of the loaf at that location.

The shape of the slice depends on how we cut it.

The cross section is the flat face of the slice (a 2D shape), not the slice of bread itself, which has thickness and is 3D.

Geometry

In geometry it is the shape made when a solid is cut through by a plane.

cylinder cross section

Example:

The cross section of a circular cylinder parallel to the base is a circle

We don't draw the rest of the object, just the shape made when we cut through.

cross-section of a pyramid

Example:

The cross section of a rectangular pyramid parallel to the base is a rectangle

Cross sections are usually parallel to the base like above, but can be in any direction.

Example:

torus cross section

The vertical cross section through the center of this torus is two circles!

torus horizontal cross section

And the horizontal cross section is an annulus

More Examples of Cross Sections

Square Prism: Cross Section:
square prism square
Cube: Cross Section:
cube square
Pentagonal Prism: Cross Section:
pentagonal prism pentagon
Polyhedron Cuboids / Rectangular Prisms Platonic Solids Cylinder Cone Sphere Torus

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