Nets of 3D Shapes –

Nets of 3D shapes is a visual topic tested at Foundation and Higher tiers across AQA, Edexcel, and OCR. You need to recognise which 2D net folds into a given 3D shape, draw accurate nets, and use nets to calculate surface area. This guide shows you the standard nets for every common 3D shape, walks through worked examples, and provides practice questions to build your confidence.

What Is a Net?

A net is a flat 2D shape that can be folded along its edges to form a 3D shape. When unfolded, each face of the 3D shape appears as a flat region in the net, and adjacent faces share an edge.

A single 3D shape can have several different valid nets. For example, a cube has 11 distinct nets.

Key Nets to Know

Step-by-Step Method

Identifying Whether a Net Folds into a Given Shape

1. Count the faces in the net — does the number match the 3D shape?
2. Check the shapes of the faces — are they the correct types (squares, triangles, rectangles)?
3. Check that no faces overlap when folded — adjacent faces must share exactly one edge and fold without collision.
4. Mentally fold the net (or use the elimination approach in multiple-choice questions) to confirm it creates the correct 3D shape.

Drawing a Net

1. Identify all faces of the 3D shape and their dimensions.
2. Start with one face (usually the base) and attach adjacent faces along shared edges.
3. Ensure all faces are connected and can fold up without overlapping.
4. Label dimensions on each face.

Worked Example 1 — Foundation Level

Question: Draw the net of a cuboid with length 5 cm, width 3 cm, and height 2 cm.

Working:

Step 1 — A cuboid has 6 faces: two 5 × 3 faces (top and bottom), two 5 × 2 faces (front and back), and two 3 × 2 faces (left and right).

Step 2 — Start with a 5 × 3 rectangle as the base. Attach a 5 × 2 rectangle to the top edge (front), a 5 × 2 rectangle to the bottom edge (back), a 3 × 2 rectangle to the left edge, and a 3 × 2 rectangle to the right edge. Finally attach the second 5 × 3 rectangle to the top of the front face.

Step 3 — The net forms a cross shape. Label all dimensions.

Answer: A cross-shaped net with faces 5 × 3, 5 × 3, 5 × 2, 5 × 2, 3 × 2, and 3 × 2.

Worked Example 2 — Higher Level

Question: A cylinder has radius 4 cm and height 9 cm. Sketch its net and find the total surface area.

Working:

Step 1 — The net of a cylinder consists of 2 circles (radius 4 cm) and 1 rectangle.

Step 2 — The rectangle has height 9 cm and width equal to the circumference of the circle: 2π × 4 = 8π cm.

Step 3 — Total surface area = 2 circles + rectangle = 2 × π × 4² + 8π × 9 = 32π + 72π = 104π ≈ 326.7 cm².

Answer: Total surface area = 104π cm² ≈ 326.7 cm².

Worked Example 3 — Exam Style

Question: A square-based pyramid has a base edge of 6 cm and a slant height of 5 cm. Draw the net and find the total surface area.

Working:

Step 1 — The net has 1 square (6 × 6) and 4 identical isosceles triangles, each with base 6 cm and slant height 5 cm.

Step 2 — Area of square = 6 × 6 = 36 cm².

Step 3 — Area of one triangle = ½ × 6 × 5 = 15 cm².

Step 4 — Total area of 4 triangles = 4 × 15 = 60 cm².

Step 5 — Total surface area = 36 + 60 = 96 cm².

Answer: Total surface area = 96 cm².

Common Mistakes

• Confusing slant height with perpendicular height. In pyramids and cones, the net uses the slant height for the triangular faces or sector, not the vertical height.
• Getting the rectangle width wrong on cylinder nets. The width of the rectangle must equal the circumference (2πr), not the diameter.
• Drawing overlapping faces. If two faces share more than one edge in your net, the net is invalid — faces will collide when folded.

Exam Tips

• If a question shows multiple nets and asks which one folds into a specific shape, eliminate options by checking face counts and dimensions first.
• For surface area questions, sketching the net is a reliable way to make sure you account for every face.
• When drawing nets on squared paper, use the grid lines to keep edges straight and lengths accurate.
• Remember that a cone's net uses a sector — the arc length of the sector equals the circumference of the base circle.

Practice Questions

Q1 (Foundation): How many faces appear in the net of a triangular prism?

Q2 (Foundation): A cube has edge length 4 cm. Find the total surface area using its net.

Q3 (Higher): A cone has base radius 3 cm and slant height 7 cm. Find the curved surface area of the cone.

Practise nets and surface area questions with instant feedback free on GCSEMathsAI.

Related Topics

• 3D Shapes: Faces, Edges and Vertices — properties of 3D shapes.
• Surface Area — calculating surface area using nets.
• Plans and Elevations — viewing 3D shapes from different directions.

Summary

Nets of 3D shapes test your ability to visualise how flat 2D patterns fold into solid shapes. Know the standard nets for cubes, cuboids, prisms, pyramids, cylinders, and cones. The most common pitfalls are using the wrong measurement for a cylinder's rectangle width and confusing slant height with perpendicular height. Sketching the net is also the most reliable method for surface area calculations, since it ensures every face is counted exactly once.