Detailed definition
Understanding Cross Sections
A cross section is the two-dimensional shape formed when a plane slices through a solid. The result depends on both the solid and the direction or position of the slice.
Cross sections are important because one solid can produce many different flat shapes. A cylinder can yield circles or rectangles in common settings, and a cone can produce several conic-section curves under special cuts.
This page keeps the solid and the slice together so the 2D result stays tied to the 3D geometry that created it.
Key facts
Important ideas to remember
- A cross section is the 2D shape formed when a solid is sliced by a plane.
- A cross section is always a 2D figure, even though it comes from a 3D object.
- Changing the plane changes the resulting section, sometimes dramatically.
- Cross sections connect solid geometry to plane geometry and, in some cases, to conic sections.
Where it is used
Where cross sections shows up
- Use cross sections when identifying the flat shape produced by slicing a prism, cylinder, cone, or sphere.
- Use them in architecture, engineering, medical imaging, and manufacturing drawings.
- Use them to connect 3D solids with familiar 2D geometry facts.
Common mistakes
What to watch out for
- Do not name the cross section from the outside look of the solid alone; the slicing plane matters.
- Do not forget that the result is two-dimensional, not a smaller 3D solid.
- Do not assume one solid has only one possible cross section.