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.