Nets of 3D Shapes
A net is a flat 2D pattern that can be folded to make a 3D shape. If you cut open a cardboard box and lay it flat, the flat shape you get is the net of the cuboid.
Different 3D shapes have different nets. Some shapes (like a cube) have multiple possible nets — a cube has 11 different nets.
What is Nets of 3D Shapes - Grade 7 Maths (Visualising Solid Shapes)?
Definition: A net of a 3D shape is a 2D figure that can be folded along its edges to form the 3D shape. When unfolded, every face of the 3D shape appears as a flat polygon in the net.
Nets of 3D Shapes Formula
Nets of common shapes:
- Cube: 6 connected squares (11 possible arrangements).
- Cuboid: 6 connected rectangles (3 pairs of identical rectangles).
- Cylinder: 2 circles + 1 rectangle.
- Cone: 1 circle + 1 sector (fan shape).
- Triangular prism: 2 triangles + 3 rectangles.
- Square pyramid: 1 square + 4 triangles.
Types and Properties
How to check if a flat pattern is a valid net:
- Count the number of faces — it must match the 3D shape.
- Check that faces connect along edges properly.
- When folded, no faces should overlap.
- All faces must be accounted for — no gaps.
Solved Examples
Example 1: Net of a Cube
Problem: A net has 6 squares. Can it always fold into a cube?
Solution:
- Not always. The 6 squares must be arranged so they fold without overlapping.
- There are exactly 11 valid nets for a cube out of 35 possible hexomino arrangements.
Answer: Only if the arrangement is one of the 11 valid cube nets.
Example 2: Net of a Cylinder
Problem: Describe the net of a cylinder.
Solution:
- A cylinder has 2 circular faces and 1 curved surface.
- The net consists of 2 circles and 1 rectangle.
- The rectangle’s length = circumference of the circle = 2πr.
Answer: 2 circles + 1 rectangle (length = 2πr, width = height of cylinder).
Example 3: Net of a Square Pyramid
Problem: How many faces appear in the net of a square pyramid?
Solution:
- 1 square (base) + 4 triangles (sides) = 5 faces.
Answer: 5 faces — 1 square and 4 triangles.
Example 4: Identifying the Shape from Net
Problem: A net has 2 triangles and 3 rectangles. What shape does it fold into?
Solution:
- 2 triangular faces + 3 rectangular faces = 5 faces total.
- This matches a triangular prism.
Answer: Triangular prism.
Real-World Applications
Real-world uses:
- Packaging: Boxes for products are cut from flat sheets using net patterns.
- Craft: Paper models and origami use nets to create 3D shapes.
- Architecture: Building models are assembled from flat nets.
- Manufacturing: Sheet metal is cut into nets and folded into 3D objects.
Key Points to Remember
- A net is a flat pattern that folds into a 3D shape.
- A cube has 11 different valid nets.
- The net of a cylinder is 2 circles + 1 rectangle.
- When folding a net, no faces should overlap.
- You can verify a net by counting faces and checking connections.
Practice Problems
- Draw a net for a cuboid with dimensions 4 cm × 3 cm × 2 cm.
- How many triangles appear in the net of a triangular pyramid (tetrahedron)?
- Can 6 squares arranged in a straight line fold into a cube?
- Describe the net of a cone.
Frequently Asked Questions
Q1. What is a net in maths?
A net is a flat 2D shape that can be folded along its edges to form a 3D shape. It shows all the faces of the 3D shape laid out flat.
Q2. How many nets does a cube have?
A cube has exactly 11 different nets. These are 11 different arrangements of 6 squares that can fold into a cube.
Q3. Can a sphere have a net?
No. A sphere has a curved surface that cannot be laid flat without stretching or cutting. Only polyhedra and shapes with flat + simple curved surfaces have exact nets.
