Nets of 3D Shapes (Grade 5)
A net is a flat (2D) pattern that can be folded to make a 3D shape. Imagine cutting open a cardboard box along its edges and unfolding it flat — the flat shape you get is the net of the box.
Nets are used in packaging, architecture, and manufacturing. Every time a company designs a new box for a product, they start with a net. The net is printed, cut, and folded to create the box.
In Class 5, you will learn to identify nets of common 3D shapes like cubes, cuboids, cylinders, cones, and pyramids. You will also learn to distinguish valid nets from invalid arrangements.
What is Nets of 3D Shapes - Class 5 Maths (Geometry)?
A net of a 3D shape is a two-dimensional figure that, when folded along its edges, forms the surface of the 3D shape. Each face of the solid appears as a flat shape in the net, connected at the correct edges.
Key facts:
- A single 3D shape can have multiple different nets (arranged differently).
- Not every arrangement of flat shapes forms a valid net — the faces must fold up without overlapping.
- A net shows all the faces of a 3D shape laid flat.
Types and Properties
Nets of Common 3D Shapes:
| 3D Shape | Faces | Net Description |
|---|---|---|
| Cube | 6 identical squares | 6 connected squares; 11 different net arrangements exist |
| Cuboid | 6 rectangles (3 pairs of equal rectangles) | 6 connected rectangles arranged so opposite faces are not adjacent |
| Cylinder | 2 circles + 1 curved surface | 2 circles + 1 rectangle (whose width = circumference of circle) |
| Cone | 1 circle + 1 curved surface | 1 circle + 1 sector (pie-shaped piece) |
| Triangular Pyramid | 4 triangles | 4 connected triangles |
| Square Pyramid | 1 square + 4 triangles | 1 square with a triangle on each side |
Solved Examples
Example 1: Example 1: Net of a Cube
Problem: How many squares are needed to make a net of a cube?
Solution:
Step 1: A cube has 6 faces.
Step 2: Each face is a square.
Step 3: The net of a cube requires 6 squares connected edge-to-edge.
Answer: 6 squares.
Example 2: Example 2: Identifying a Cube Net
Problem: Aman arranges 6 squares in a cross shape (one in the centre, one on each side, and one on top). Is this a valid net of a cube?
Solution:
Step 1: A cross-shaped arrangement has 1 square in the middle, 4 squares on each side, and 1 more extending from one side.
Step 2: When folded, each square becomes a face. Check: no two squares overlap when folded.
Step 3: The cross shape is one of the 11 valid nets of a cube.
Answer: Yes, it is a valid net of a cube.
Example 3: Example 3: Invalid Net
Problem: 6 squares are arranged in a row (a 1 × 6 strip). Is this a valid cube net?
Solution:
Step 1: Try to fold a 1 × 6 strip into a cube.
Step 2: After folding 4 squares into a tube, 2 squares are left. They both try to cover the same face (top), causing overlap.
Answer: No, a 1 × 6 strip is not a valid cube net.
Example 4: Example 4: Net of a Cuboid
Problem: A cuboid has length 5 cm, breadth 3 cm, and height 2 cm. Describe its net.
Solution:
Step 1: A cuboid has 6 rectangular faces: two 5×3, two 5×2, and two 3×2.
Step 2: The net is 6 rectangles connected at edges: a row of four rectangles (5×3, 5×2, 5×3, 5×2) with the two 3×2 rectangles attached to one of the 5×3 rectangles.
Answer: The net has 6 rectangles: two measuring 5×3, two measuring 5×2, and two measuring 3×2 cm.
Example 5: Example 5: Net of a Cylinder
Problem: What shapes make up the net of a cylinder?
Solution:
Step 1: A cylinder has 2 circular faces (top and bottom) and 1 curved surface.
Step 2: When unrolled, the curved surface becomes a rectangle.
Step 3: The width of the rectangle equals the circumference of the circle.
Answer: The net of a cylinder is 2 circles and 1 rectangle.
Example 6: Example 6: Net of a Cone
Problem: What shapes make up the net of a cone?
Solution:
Step 1: A cone has 1 circular base and 1 curved surface.
Step 2: When unrolled, the curved surface becomes a sector (a pie-shaped piece of a circle).
Answer: The net of a cone is 1 circle and 1 sector.
Example 7: Example 7: Net of a Triangular Pyramid
Problem: A triangular pyramid (tetrahedron) has all faces as equilateral triangles. How many triangles are in its net?
Solution:
Step 1: A tetrahedron has 4 triangular faces.
Step 2: Its net consists of 4 connected equilateral triangles.
Answer: 4 equilateral triangles.
Example 8: Example 8: Net of a Square Pyramid
Problem: Priya wants to make a square pyramid from cardboard. What shapes does she need to cut?
Solution:
Step 1: A square pyramid has 1 square base and 4 triangular faces.
Step 2: The net has 1 square with a triangle attached to each of its 4 sides.
Answer: She needs 1 square and 4 triangles.
Example 9: Example 9: Matching Net to Shape
Problem: A net has 2 circles and 1 rectangle. Which 3D shape does it form?
Solution:
Step 1: 2 circles = top and bottom faces. 1 rectangle = the curved surface when rolled.
Step 2: This is the net of a cylinder.
Answer: Cylinder.
Example 10: Example 10: Counting Cube Nets
Problem: How many different nets can a cube have?
Solution:
Step 1: Mathematicians have found that there are exactly 11 different ways to arrange 6 squares into a valid cube net.
Step 2: Each arrangement folds into the same cube, but the flat pattern looks different.
Answer: A cube has 11 different nets.
Real-World Applications
Where are nets used?
- Packaging: Cardboard boxes, cereal packets, toothpaste boxes — all start as flat nets that are folded and glued.
- Gift wrapping: Understanding nets helps you wrap oddly shaped gifts efficiently.
- Maths and surface area: To calculate the surface area of a 3D shape, you can flatten it into a net and find the total area of all faces.
- Architecture: Architects use nets (called development drawings) to plan how sheet materials will fold into 3D structures.
- Origami and paper craft: Many paper models start from flat nets that are folded into animals, buildings, and shapes.
Key Points to Remember
- A net is a flat 2D pattern that folds into a 3D shape.
- A cube net has 6 squares. There are 11 possible cube net arrangements.
- A cuboid net has 6 rectangles (3 pairs of equal rectangles).
- A cylinder net has 2 circles + 1 rectangle.
- A cone net has 1 circle + 1 sector.
- A triangular pyramid net has 4 triangles.
- A square pyramid net has 1 square + 4 triangles.
- Not every arrangement of faces makes a valid net — faces must fold without overlapping or leaving gaps.
- Nets help us calculate surface area (total area of all faces).
Practice Problems
- Draw a net for a cube on grid paper. Cut it out and fold it to verify.
- A cuboid is 4 cm long, 3 cm wide, and 2 cm tall. Sketch its net and label the dimensions on each face.
- Can a 2 × 3 arrangement of squares form a cube net? Why or why not?
- How many faces does a triangular prism have? Describe its net.
- Identify the 3D shape: its net has 1 square and 4 identical triangles.
- Which 3D shape has a net made of 2 circles and 1 rectangle?
- Draw two different nets for the same cube.
- Dev says a cube net always looks like a cross. Is he correct?
Frequently Asked Questions
Q1. What is a net of a 3D shape?
A net is a flat (2D) pattern made up of the faces of a 3D shape, connected at their edges. When folded along the edges, it forms the 3D shape.
Q2. How many nets does a cube have?
A cube has exactly 11 different nets. Each is a different arrangement of 6 connected squares that folds into a cube.
Q3. What shapes are in the net of a cylinder?
The net of a cylinder consists of 2 circles (top and bottom) and 1 rectangle (the curved surface unrolled). The rectangle's width equals the circumference of the circle.
Q4. How do I check if a net is valid?
Cut out the pattern and try to fold it. If it forms the 3D shape without any faces overlapping or any gaps, it is a valid net. You can also check mentally that opposite faces are not adjacent in the net.
Q5. What is the net of a cone?
The net of a cone is 1 circle (the base) and 1 sector (a pie-shaped piece that wraps into the curved surface of the cone).
Q6. Can a 3D shape have more than one net?
Yes. Most 3D shapes have multiple valid nets. For example, a cube has 11 different nets, and a cuboid has even more.
Q7. What is the difference between a net and a 3D shape?
A net is flat (2-dimensional) and shows all the faces of the shape laid out. A 3D shape is the solid object itself. The net folds into the 3D shape.
Q8. Why are nets useful?
Nets help us understand the structure of 3D shapes, calculate surface area, and make models. Packaging designers use nets to design cardboard boxes.
Q9. How many faces does a cuboid net show?
A cuboid net shows 6 rectangles — 3 pairs of equal rectangles, one pair for each dimension (length×breadth, length×height, breadth×height).
Q10. Is this topic in the NCERT Class 5 syllabus?
Yes. Nets of 3D shapes are part of the Geometry chapter in NCERT/CBSE Class 5 Maths, building on the understanding of 3D shapes from earlier classes.
Related Topics
- 3D Shapes (Grade 2)
- Views of 3D Shapes (Grade 5)
- Lines, Line Segments and Rays
- Parallel and Perpendicular Lines
- Angles (Grade 5)
- Angle Sum Property of Triangle
- Types of Triangles (Grade 5)
- Quadrilaterals (Grade 5)
- Circles (Grade 5)
- Symmetry (Grade 5)
- Reflection and Rotation
- Complementary and Supplementary Angles
