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Grade 7 Math Lab: The Algebraic Pivot FREE
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Cross-Sections of 3D Shapes
Learning Objectives
- Identify cross-sections
- Relate 2D slices to 3D solids
- Describe resulting shapes
Key Concepts
Cross-Section
The 2D shape formed by slicing a 3D solid with a plane
Plane
A flat surface that extends infinitely
Theory
**Common cross-sections:**
- Sphere sliced by any plane → Circle
- Cylinder sliced parallel to base → Circle
- Cylinder sliced perpendicular to base → Rectangle
- Cone sliced parallel to base → Circle
- Cone sliced through apex → Triangle
- Rectangular prism → Rectangle, triangle, or other polygon depending on angle
Examples
Slice a cube diagonally corner to corner
Solution: Creates a rectangular (or triangular) cross-section