A net is a flat (2D) shape that can be folded along its edges to form a 3D solid. Think of it as the shape unfolded flat — like opening out a cardboard box.
Net = the 3D shape unfolded into a flat 2D pattern Every face of the solid appears exactly once in the net
Example 1 — How many faces does a cube's net contain? What shape are they?
Step 1
A cube has 6 faces, so its net must contain exactly 6 squares.
Step 2
All 6 squares are equal in size (side length = edge length of the cube).
Step 3
There are 11 different arrangements of 6 squares (hexominoes) that fold into a cube. The cross shape is one of the most common.
Example 2 — Describe the net of a cuboid with length 8 cm, width 5 cm, height 3 cm
Step 1
A cuboid has 3 pairs of identical rectangular faces.
Pair 3 (left/right): \(5 \times 3 = 15 \text{ cm}^2\) each — total 6 rectangles in the net
Key insight: The net of any shape must contain exactly the same number of faces as the 3D shape, and each face appears exactly once. If you count them in the net, they must match the shape's face count.
✓ Quick Check 1 — Nets of Cubes and Cuboids
Question 1 of 10
Nets of Triangular Prisms and Cones
Other common 3D shapes also have distinctive nets. Understanding these helps you calculate surface area and design packaging.
Example 3 — Describe the net of a triangular prism
Step 1
A triangular prism has 5 faces: 2 triangular ends and 3 rectangular side faces.
Step 2
The net consists of: 2 triangles (the end faces) + 3 rectangles (the side faces).
Step 3
The 3 rectangles all have the same height (= length of the prism). Their widths equal the 3 sides of the triangular end.
Step 4
The triangles sit at either end of the strip of three rectangles.
Example 4 — Describe the net of a cone with base radius \(r\) and slant height \(l\)
Step 1
A cone has 2 surfaces: a flat circular base and a curved surface.
Step 2
When unrolled flat, the curved surface becomes a sector (a slice of a large circle).
Step 3
The sector has radius equal to the slant height \(l\) of the cone.
Step 4
The arc length of the sector equals the circumference of the base circle: \(2\pi r\).
Common error: Students often forget the base circle when drawing the net of a cone. The net has TWO parts: the sector AND the circle — both are needed to close the cone.
✓ Quick Check 2 — Nets of Prisms and Cones
Question 1 of 10
Valid and Invalid Nets — Packaging and Real-Life Applications
Not every arrangement of faces is a valid net. In packaging and manufacturing, choosing the right net saves material and ensures the shape folds correctly.
Example 5 — Is a row of 6 squares in a straight line a valid net of a cube?
Step 1
Label the 6 squares in the row 1–6. Imagine folding: square 1 becomes the front, 2 the top, 3 the back, 4 the bottom.
Step 2
Squares 5 and 6 would both try to become the same face (front again) — they overlap.
Step 3
This is an invalid net — faces overlap when folded, so it cannot form a cube.
Example 6 — A packaging designer needs a net for a box 30 cm × 20 cm × 10 cm. What faces does the net include?
Step 1
The box is a cuboid: 3 pairs of faces.
Step 2
Top and bottom: \(30 \times 20 = 600 \text{ cm}^2\) each — two of these.
Step 3
Front and back: \(30 \times 10 = 300 \text{ cm}^2\) each — two of these.
Step 4
Left and right: \(20 \times 10 = 200 \text{ cm}^2\) each — two of these. Net total area = \(2(600+300+200) = 2200 \text{ cm}^2\).
Test for a valid net: Try to mentally fold each face. Check (1) no two faces overlap when folded, (2) every face of the 3D shape is represented exactly once, (3) the net is one connected piece.
✓ Quick Check 3 — Valid Nets and Packaging Applications
Question 1 of 10
Practice
Work out each answer, then type it in and click Check to see if you're right.
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Question
Your answer
Result
1
How many faces does a cube net have?
2
A net has 2 circles and 1 rectangle. What 3D shape does it make?
3
How many rectangles are in the net of a cuboid?
4
A net has 1 square and 4 triangles. What 3D shape does it make?
5
How many faces does the net of a triangular prism have?
6
A net has 2 triangles and 3 rectangles. What shape does it fold into?
7
How many faces does a square-based pyramid net have?
⚠ Things to Watch Out For
Not every arrangement of faces folds into a valid net — check that opposite faces will align correctly when folded.
Count the number of faces — a cuboid has 6, a triangular prism has 5, a square-based pyramid has 5.
The orientation of each face matters — if a face is rotated incorrectly in the net, it won't fold together properly.
Distinguish between prisms (which have two identical ends and rectangular sides) and pyramids (which have a base and triangular sides meeting at a point).
There are often multiple valid nets for the same shape — don't assume only one arrangement is correct.