Curriculum placement
Grade 7. This describes the skill, not a learner estimate.
Cross-sections of solids
Identify plane cross-sections of solids
Problem types
- Name a cross-section
- Area of a cross-section
- Shape that cannot be a plane section of a solid
Builds on
- Surface area of prisms and pyramids
- Sides, angles, and faces · Useful idea
A cross-section of a solid is a polygon, named by its sides and angles.
Leads to
- Cross-sections and solids of revolution
- Cavalieri's principle · Extend the idea
Slicing a solid gives cross-sections at every height, and equal cross-sections at every height give equal volumes.
- Conic sections and their equations · See it applied
Slicing a cone with a plane gives a circle, an ellipse, a parabola or a hyperbola, the conic sections.
Related skills
- Area and volume of composite figures · Shared foundations
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