Topics · Primary Maths · 3D Solids & Nets
3D solids and their nets
A solid takes up space, so it cannot lie flat on a page. A net is what you get by cutting it open and unfolding it — the flat shape that folds back up into the solid.
- 150 exam papers analysed
- appears in 63% of P6 Maths papers
- ~4 min read
01 Faces, edges and vertices
Every solid with flat sides is described by three counts, and papers ask for them constantly.
A face is a flat surface. An edge is where two faces meet. A vertex is a corner where edges meet — the plural is vertices, not vertexes.
A cuboid has 6 faces, 12 edges and 8 vertices, and so does a cube, because a cube is just a cuboid with equal edges. Count them on the drawing: three faces you can see and three you cannot.
02 What a net is
Cut along enough edges of a solid and it opens out flat. That flat shape is its net, and folding the net back up gives you the solid again.
A cube has six square faces, so its net is always six squares joined edge to edge. But not every arrangement of six squares works — and that is the whole difficulty.
03 Nets that do not work
These are also six squares joined edge to edge, and neither folds into a cube. Both are worth looking at, because both are the answers children pick.
The test is whether the six squares reach six different faces. Fold the first one up and two squares try to land on the same face, leaving another face open — the box has a hole and an overlap at the same time.
04 How to check a net without folding it
In an exam you cannot cut the page up, so you need a way to test one in your head. These three checks catch nearly every wrong answer.
- Count the squares. A cube net has exactly six. Fewer or more and you can stop.
- Look for a 2 by 2 block. Four squares in a square can never fold — they would wrap round and overlap. Any net containing one is out.
- Find the opposite pairs. On a cube, opposite faces never touch. In a row of four, the 1st and 3rd are opposite, and so are the 2nd and 4th. If two squares that must be opposite are joined edge to edge, the net cannot work.
- Check no more than four in a line. Four in a row wraps exactly once round the cube. Five or six in a line means at least one square lands on a face already used.
05 How to say them
These are words most children have never said out loud, and a word you cannot say is a word you avoid using. Capitals mark the syllable you lean on. Tap the speaker to hear it.
- facemore than onefaces
A flat surface of a solid. A cube has six, all of them squares.
- edgemore than oneedges
The line where two faces meet. A cube has twelve.
- vertexsayVUR-teksmore than onevertices
A corner where edges meet. A cube has eight. The plural is vertices — not vertexes.
- netmore than onenets
The flat shape you get by unfolding a solid. Folding it back up gives the solid again.
- cuboidsayKYOO-boydmore than onecuboids
A box shape with six rectangular faces and every corner a right angle.
- prismsayPRIZ-uhmmore than oneprisms
A solid with the same shape all the way through, so both ends match. A cuboid is a prism whose ends are rectangles.
- pyramidsayPI-ruh-midmore than onepyramids
A solid with a flat base whose other faces are triangles meeting at a single point above it.
06 What each level is tested on
The same topic, asked differently as it goes up. The percentage is the share of papers at that level in which it appears.
- P2
Naming solids — cube, cuboid, cylinder, cone, sphere — and sorting them by shape.
Practise P2 3D Solids & Nets — 10 questions →41% of P2 papers
- P5
Counting faces, edges and vertices, and matching a solid to its net.
Practise P5 3D Solids & Nets — 10 questions →39% of P5 papers
- P6
Choosing which of several nets folds into a given cube or cuboid, and working out which face lands opposite which.
Practise P6 3D Solids & Nets — 10 questions →63% of P6 papers
07 Mistakes worth knowing about
Each of these is wrong. Decide why before you open it.
“A cube has 6 faces, 6 edges and 6 vertices.”
Six faces, but twelve edges and eight vertices. Count the edges on a drawing: four round the top, four round the bottom, four uprights.
“Any six squares joined together make a cube net.”
Only eleven arrangements work. A 2 by 3 block is six squares joined edge to edge and folds into nothing at all.
“The plural of vertex is vertexes.”
It is vertices. Papers use that word, so it is worth reading correctly as well as writing.
“A cube and a cuboid are different shapes.”
A cube is a cuboid whose edges happen to be equal, the same way a square is a rectangle. Every cube is a cuboid.
“This net has a 2 by 2 block in it, but it still looks foldable.”
It is not. Four squares in a square wrap right round and overlap, so no net containing a 2 by 2 block can fold into a cube.
Now try it
30 questions across 3 levels, marked as you go with the working shown.