Net of a Cuboid

What is a Net?

A net is a two-dimensional representation of a three-dimensional solid. For a cuboid, the net shows all its rectangular faces laid out flat, connected along their edges. When folded, the net forms the cuboid.

Net of a Cuboid

A cuboid has:

1. 6 rectangular faces: Opposite faces are identical.
2. 12 edges: Each edge represents a connection between two faces.
3. 8 vertices: Points where edges meet. To create the net of a cuboid:

• Identify the dimensions of the cuboid (length $l$, width $w$, height $h$).
• Arrange six rectangles so they can fold into a 3D shape with the specified dimensions.

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Applications of Nets

• Calculating Surface Area: The total area of all the rectangles in the net gives the surface area of the cuboid.

$$\text{Surface Area} = 2lw + 2lh + 2wh$$

• Design and Construction: Nets are used in packaging design, where materials need to be cut and folded into the required 3D shape.

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Worked Example

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Summary

• Net of a Cuboid: A 2D arrangement of its six rectangular faces.
• Surface Area Calculation: Add the areas of all rectangles in the net.

$$\text{Surface Area} = 2lw + 2lh + 2wh$$

• Applications: Used in construction, design, and packaging.
• Practice creating nets to visualize and solve geometry problems effectively.