Unit 10 · Measurement and Three-Dimensional Geometry

10.10Cross Sections of Three-Dimensional Figures

Quick Answer

A cross section is the intersection of a plane with a solid. Cutting a cylinder parallel to the base gives a circle; perpendicular gives a rectangle. Cutting a cone at an angle can give an ellipse, parabola, or hyperbola.

Essential Question

How does the angle and position of a cutting plane determine the shape of the cross section of a three-dimensional solid?

Learning Goals

  • 1Define cross section.
  • 2Identify cross sections of prisms and cylinders.
  • 3Identify cross sections of pyramids and cones.
  • 4Identify cross sections of spheres.
  • 5Describe how changing the cutting plane changes the cross section.

Key Vocabulary

Cross section

The two-dimensional shape formed by the intersection of a plane with a three-dimensional solid.

Conic section

A cross section of a cone: circle, ellipse, parabola, or hyperbola, depending on the angle of the cut.

Full lesson content coming soon

Worked examples, guided practice problems, a workbook, quiz, and downloadable PDF resources will be added to this lesson in Phase 2. The learning goals and vocabulary above reflect the complete lesson scope.