Nets of 3D Shapes – Unfolding a Solid Flat
A net is a 2D pattern that can be folded up to form a 3D solid, showing every face laid out flat and connected at the edges where they'll eventually join. Nets are how flat cardboard becomes a cereal box, and they're a powerful way to actually see every one of a solid's faces at once, rather than imagining the hidden ones around the back.
Only flat-faced solids (polyhedra) have true nets made of separate flat pieces – a cube's net is 6 connected squares, and a square pyramid's net is 1 square plus 4 triangles. Curved solids like cylinders and cones have a mix of flat and curved pieces in their nets.
Reading a Net
A net shows all of a solid's faces unfolded and connected. The number of pieces in a net always matches the number of faces on the solid.
2 circular ends plus 1 curved side: this net folds into a cylinder.
Real-Life Application
- Packaging design: cereal boxes and cartons are designed and cut as flat nets.
- Origami: paper folding relies on the same fold-a-flat-shape-into-a-solid idea.
- Architecture models: architects build paper models from nets of building shapes.
Key Takeaways
- A net is a flat 2D pattern that folds up into a 3D solid.
- The number of pieces in a net matches the solid's number of faces.
- Curved solids like cylinders and cones have nets with both flat and curved pieces.
Practice: Nets of 3D Shapes
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