Nets of 3D shapes KS3 questions ask you to recognise or draw the flat, 2D pattern that folds up into a solid shape. Each face of the 3D shape appears once in the net, joined along edges so that folding brings matching edges together with no gaps or overlaps.
What is a net?
A net is a two-dimensional shape that can be folded along its edges to form a three-dimensional solid, with no overlapping faces and no gaps. Every face of the solid appears exactly once in the net, drawn at its true size and shape. Nets are useful because they let you calculate surface area (the total area of all the faces) by working entirely in 2D, adding up the area of each face in the flat pattern.
Not every arrangement of the correct faces makes a valid net — the faces also need to be positioned so that folding actually closes the shape without any face colliding with another.
What faces make up the net of common 3D shapes?
Each solid has a fixed set of faces that its net must contain. Here is the face count and shape for the solids most often tested at KS3:
| 3D shape | Faces in the net | Shape of each face |
|---|---|---|
| Cube | 6 squares | All identical squares |
| Cuboid | 6 rectangles | 3 pairs of equal rectangles |
| Triangular prism | 2 triangles + 3 rectangles | Triangular ends, rectangular sides |
| Square-based pyramid | 1 square + 4 triangles | Square base, triangular sides |
| Cylinder | 2 circles + 1 rectangle | Circular ends, curved surface unrolled flat |
| Cone | 1 circle + 1 sector | Circular base, curved surface as a sector |
What does the net of a cube look like?
A cube has 6 identical square faces, and there are 11 different valid arrangements of 6 squares that fold into a cube — but many more arrangements of 6 squares do not fold correctly (faces overlap, or a gap is left open). The most familiar cube net is a "cross" shape: one square in the centre with a square attached to each side, plus one more square attached above or below one of those.
To check whether an arrangement of squares is a valid cube net, imagine folding each square up along its shared edges one at a time and track where each face ends up — a valid net closes into a cube with every face used once and no face landing on top of another.
What does the net of a cylinder look like?
The net of a cylinder has three parts: two identical circles (the top and bottom) and one rectangle (the curved surface, unrolled flat). The key relationship students often miss is that the width of the rectangle equals the circumference of the circle — because that curved rectangle wraps exactly once around the circular ends when folded.
Worked example: A cylinder has a circular base of radius 3 cm and a height of 10 cm. Find the surface area using its net.
- Area of the two circular ends: $2 \times \pi r^2 = 2 \times \pi \times 3^2 = 18\pi \approx 56.5 \text{ cm}^2$
- Circumference of the circle (width of the curved rectangle): $2\pi r = 2 \times \pi \times 3 = 6\pi \approx 18.8 \text{ cm}$
- Area of the curved rectangle: $6\pi \times 10 = 60\pi \approx 188.5 \text{ cm}^2$
- Total surface area: $18\pi + 60\pi = 78\pi \approx 245.0 \text{ cm}^2$ (to 1 decimal place)
What does the net of a triangular prism look like?
A triangular prism's net has five faces: two triangles (the identical triangular ends) and three rectangles (the sides connecting them). Each rectangle's length matches the length of the prism, and each rectangle's width matches one side of the triangular cross-section — so the three rectangles are usually different widths unless the triangle is equilateral.
A common KS3 task is matching a given net back to its solid by checking that each rectangle's width lines up with the correct triangle side once folded.
How do you identify whether a diagram shows a valid net?
Use these checks whenever you're shown an arrangement of shapes and asked if it folds into a given solid:
- Count the faces. The number of shapes in the net must match the number of faces on the solid (6 for a cube or cuboid, 5 for a triangular prism or square pyramid, and so on).
- Match the face shapes. Each face's shape and size must correspond to a real face on the solid — a cube net cannot include a rectangle unless it is also a square.
- Trace the fold. Mentally fold each face along its edges in turn; if two faces would land on top of each other, or a gap is left uncovered, the net is invalid.
Frequently asked questions
How many different nets does a cube have?
A cube has exactly 11 distinct nets — 11 different arrangements of 6 squares that fold up correctly with no overlaps or gaps. Many more arrangements of 6 connected squares exist, but most of them do not fold into a closed cube.
Why does the rectangle in a cylinder's net have to match the circumference?
The rectangle forms the curved side of the cylinder, and it must wrap exactly once around each circular end when folded. If its width didn't equal the circle's circumference, the rectangle would either fail to meet itself all the way round or overlap itself, so the fold wouldn't close cleanly into a cylinder.
Can a net be used to find volume as well as surface area?
No — a net only shows the flat faces of a solid, so it gives you the information needed for surface area (the total area of all faces), not volume. Volume depends on the 3D space enclosed by the solid, which requires a separate formula such as length × width × height for a cuboid.
What is the difference between a net and a plan-and-elevation drawing?
A net unfolds a 3D shape into its separate 2D faces so it can be reassembled by folding. A plan-and-elevation drawing instead shows the solid from fixed viewpoints (from above, from the front, from the side) without unfolding it — the shape stays whole, and you're viewing it rather than flattening it.
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