3D shapes
Nets
Unfold a cube and lay it flat, and you get a net. There are eleven different ways to do it — and plenty of arrangements that do not work at all.
A net of 6 squares folds up into a cube
What a net is
A NET is what a 3D shape looks like unfolded and laid flat. Fold the net back up along its lines and you rebuild the shape. Every face of the shape appears exactly once in its net. A cube's net always has 6 squares, because a cube has 6 faces.
Not every arrangement works
Six squares joined together is NOT automatically a net of a cube. A net fails if two squares would land on top of each other when you fold it, or if a face is left missing. Four squares in a square block, for instance, cannot fold into a cube. There are 11 different nets of a closed cube. An OPEN cube — a box with no lid — has 5 faces, so its nets have 5 squares.
Testing a net in your head
Pick one square to be the BASE. Fold the squares next to it up to make the sides. Then see whether the last square lands neatly on top as the lid. If two squares try to occupy the same place, it is not a net. If you are unsure, draw it, cut it out and fold it. That settles it every time.
Drawing 3D shapes
As well as unfolding shapes, you can draw them. ISOMETRIC PAPER has a grid of dots that makes drawing cubes and cuboids much easier — the lines slope in fixed directions so the shape looks solid. Drawing the same cuboid resting on a different face gives a different picture of the same shape.
Worked examples
How many squares in a cube's net?
- A cube has 6 faces.
- Every face appears exactly once in the net.
Answer: 6 squares
How many squares in an open cube's net?
- An open cube is a box with no lid.
- That is 6 faces minus the missing top.
Answer: 5 squares
Testing an arrangement
- Choose one square as the base.
- Fold the neighbouring squares up as sides.
- Check whether two squares would overlap.
Answer: If any two overlap, it is not a net
Faces in the net of a triangular prism
- A triangular prism has 2 triangles and 3 rectangles.
- Each face appears once in the net.
Answer: 2 triangles and 3 rectangles
Why four squares in a block will not work
- Fold three of them up around the fourth.
- There is nothing left to make the remaining sides.
- A cube needs 6 faces, not 4.
Answer: It is not a net of a cube
Where you see this in real life
- A cardboard box arrives flat as a net and is folded into shape.
- Chocolate boxes and cereal packets are designed as nets before they are printed.
- Paper models and origami start from a flat net that folds into a solid.
Key words
- Net
- A 3D shape unfolded and laid flat.
- Face
- A flat surface of a 3D shape.
- Fold line
- A line in a net where the shape bends.
- Closed cube
- A cube with all 6 faces.
- Open cube
- A box with 5 faces and no lid.
- Isometric paper
- Dotted paper that makes drawing 3D shapes easier.