Math Playground
Geometry

Cross-sections

Slice a 3D shape with a plane — what 2D shape falls out?

A cross-section is the 2D shape you see when you slice a 3D object with a flat plane. Cut an apple, a salami or a tree trunk and the slice is a cross-section.

Slicing a cone

  • Slice parallel to the base → a circle.
  • Slice at a slant → an ellipse.
  • Slice parallel to the side → a parabola.
  • Slice straight down through the apex → two intersecting lines.

The cross-sections of a cone are exactly the conic sections — that's literally where the name comes from.