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Academy11+

11+ Maths · Topic explained

3D shapes and nets

How do you make a box from one flat piece of card?

The big idea

A net is a 3D shape unfolded flat: fold it up and the faces meet edge to edge.

Picture it

Like a cereal box opened out flat, then folded back up.

Key words

face
A flat surface of a 3D shape.
edge
Where two faces meet.
vertex
A corner where edges meet (plural: vertices).
prism
The same shape all the way through, like a tent or a chocolate bar box.

Worked examples

  1. 1Warm-up

    How many faces, edges and vertices does a cube have?

    • 6 square faces
    • 12 edges
    • 8 vertices
  2. 211+ standard

    This net folds into a dice. Which number is opposite the 2?

    • In a cross-shaped net, faces with one square between them are opposite
    • 2 and 5 are opposite (and 2 + 5 = 7, like a real dice)
  3. 311+ standard

    How many faces, edges and vertices does a square-based pyramid have?

    • 1 square + 4 triangles = 5 faces
    • 4 round the base + 4 up to the top = 8 edges
    • 4 base corners + the top = 5 vertices
  4. 411+ standard

    Will six squares in a 2 by 3 rectangle fold into a cube?

    • No: when you fold it, faces overlap and two sides stay open
    • Only 11 different nets make a cube

The common mistake

The mistake

Any six squares joined together make a net of a cube.

Instead

Only 11 arrangements work: picture folding it, and check no two faces land in the same place.

Why: A row of five squares, or a 2 by 3 block, has faces that overlap when folded.

Where it comes up in the 11+

Count faces, edges and vertices; pick the net that folds into a shape; find opposite faces.

The video

Video coming soon

We're making a short video that explains 3d shapes and nets step by step. Until then, everything it covers is on this page.

Free printable

3D shapes and nets worksheet

Practice questions on this topic to print and try on paper, at home or on the way to school.

Download the worksheet (PDF)

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Quick quiz

Have a go first, then tap to see the answer.

  1. 1. How many edges does a cuboid have?

    • 6
    • 8
    • 12
    • 24
    Show the answer

    12

    4 on top, 4 underneath and 4 going up the sides.

  2. 2. How many faces does a triangular prism have?

    • 3
    • 5
    • 6
    • 9
    Show the answer

    5

    2 triangles at the ends and 3 rectangles round the sides.

  3. 3. How many vertices does a square-based pyramid have?

    • 4
    • 5
    • 8
    • 6
    Show the answer

    5

    4 corners of the square base and 1 at the top.