Nets and 3D Shape Reasoning
A net is a 2D shape that can be folded up to make a closed 3D solid. 11+ papers test recognising which net folds into a given cuboid, cube, prism or pyramid, working out which faces end up opposite each other once a net is folded, and counting the faces, edges and vertices of common 3D shapes, sometimes using the rule that links them.
Before you start
Make sure you're comfortable with these topics first:
Method
- Learn the names and properties of common 3D shapes: cube, cuboid, triangular prism, square-based pyramid and cylinder, including how many faces, edges and vertices each one has.
- Learn Euler's rule linking faces, vertices and edges of a solid: faces + vertices = edges + 2, which can check whether given numbers for a solid are consistent.
- To check whether a net folds into a closed solid, first count the faces in the net and check this matches the number of faces on the target solid, then imagine folding each face up along its edges.
- For a cube net, remember that in a straight row of four squares, the 1st and 3rd squares become opposite faces once folded, and the 2nd and 4th squares become opposite faces, not the 1st and 4th.
- Any extra squares attached above or below the row fold up or down to become the cube's top and bottom faces, which are always opposite each other, whichever row-square they are attached to.
- When a net includes markings, letters or patterns on its faces, track carefully which way each face is facing as it folds, since a face can end up upside down or sideways on the finished solid.
Worked example
A cube net is a row of four squares labelled A, B, C, D from left to right, with a fifth square, E, attached above B, and a sixth square, F, attached below C. When the net is folded into a cube, which face is opposite face A?
- The four squares in the row, A, B, C, D, fold around to form the four side faces of the cube in a ring.
- In a ring of four faces, the 1st and 3rd faces become opposite each other, and the 2nd and 4th faces become opposite each other, not the 1st and 4th, which actually end up next to each other once folded.
- Since A is the 1st square in the row and C is the 3rd, A and C become opposite faces.
- The two extra squares, E, attached above B, and F, attached below C, fold up and down to become the cube's top and bottom faces, so E and F are opposite each other, separately from the A/C and B/D pairs.
- So the face opposite A is C.
Practice questions
Type your answer and press Check to be marked straight away, or reveal the answer and mark yourself.
Q1How many faces does a cube have?Show answer
Answer: 6
Q2How many vertices does a cube have?Show answer
Answer: 8
Q3How many edges does a triangular prism have?Show answer
Answer: 9
Q4A cuboid has three different rectangular face sizes. How many faces of each size does it have?Show answer
Answer: 2 faces of each of the three sizes, giving 6 faces in total, arranged in 3 opposite pairs.
Q5A square-based pyramid has 5 faces. How many of these faces are triangles?Show answer
Answer: 4 (the fifth face is the square base)
Q6Use Euler's rule, faces + vertices = edges + 2, to find the number of edges of a solid with 5 faces and 5 vertices.Show answer
Answer: 8 edges (5 + 5 = 10 = edges + 2, so edges = 8)
Q7A net is a straight row of six identical squares. Could this fold into a closed cube? Explain briefly.Show answer
Answer: No. Folding a straight strip of six squares wraps some faces over each other while leaving other parts of the cube completely uncovered, so it does not close up correctly; a valid cube net needs its six squares arranged in shapes such as a cross or a staircase, not a single straight line.
Q8A cylinder is unfolded into its net. What two shapes make up a cylinder's net?Show answer
Answer: Two circles (the top and bottom) and one rectangle (the curved surface).
Exam-style questions
Written in the style of a 11+ exam paper, with a full mark scheme.
A shape is described as a net for a cube. It consists of a row of four squares labelled J, K, L, M, with a fifth square, N, attached above K. State how many faces a cube net must have, explain whether this net could fold into a complete, closed cube, and if not, say what is missing.
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 3 available
A cube net is a row of four squares labelled W, X, Y, Z from left to right, with a fifth square, P, attached above X, and a sixth square, Q, attached below Y. (a) Which face is opposite W? (b) Which face is opposite P?
Show mark scheme
Tick each line you got. Your score builds from the marks on the scheme.
Nothing ticked yet - 4 available
Free printable worksheet
Want more practice on paper? Download the nets and 3d shape reasoning worksheet pack - 6 pages of exam-style questions with a full mark scheme. One email opens every download in this browser for 14 days - no account, no card. Print it for personal and classroom use.
This topic is chapter 35 of 11+ Maths Workbook 2, the whole course as one free printable PDF.
Next topics
Not quite what you needed?
Tell us what is missing on nets and 3d shape reasoning, or which topic to write up next. Every request is read, and we reply to every one.
Build a full practice pack.
This topic is one of hundreds in the library - pick the ones a student needs and generate a printable PDF in minutes.