Identify the Correct Net Pattern: Cube Unfolding Analysis

Q: How many squares should a cube net have?

A cube net must have exactly 6 squares - one for each face of the cube. Having 5 squares means a missing face, while 7+ squares would create overlapping when folded.

Q: Can squares connect at corners only?

No! Squares must be connected along their edges, not just touching at corners. Corner connections won't hold the cube together when folded.

Q: Are there different valid cube net shapes?

Yes! There are 11 different valid cube nets. The T-shape is just one example - cross shapes, straight lines of 6, and L-shapes can also work.

Q: How can I test if a net will fold correctly?

Try mental folding: imagine folding each square up to form cube faces. If any faces would overlap or leave gaps, the net is invalid.

Q: What makes Choice 3 wrong if it has 6 squares?

Even with 6 squares, the arrangement matters! Some patterns create gaps or overlaps when folded. Always check if the pattern can fully enclose a 3D space.

Net Patterns with Six Connected Squares

Which of the following figures represents an unfolded cube?

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations

00:00 Choose which net belongs to a cube

00:03 We'll mark the nets that correspond to a cube, according to construction

00:06 That is, 6 faces, and there's a possibility to assemble a cube

00:10 And this is the solution to the question

Step-by-step written solution

Follow each step carefully to understand the complete solution

Understand the problem

Which of the following figures represents an unfolded cube?

Step-by-step solution

To determine which figure represents an unfolded cube, we need to ensure the following:

The figure must consist of exactly 6 squares.
The squares must be connected along their edges to allow the figure to fold into a cube without overlapping.

Let's examine each of the choices:

Choice 1: This figure consists of 6 squares arranged in a "T" shape. By folding the squares, we can form a cube, which is a valid unfolded cube shape.
Choice 2: This figure consists of only 5 squares, which is insufficient to form a cube.
Choice 3: This figure also has 6 squares, but the arrangement will not form a cube since the squares aren't in a connected format that allows a full enclosure.
Choice 4: This figure consists of 7 squares, having an extra square, which invalidates it as a cube net.

Therefore, after examining all options, we conclude that Choice 1 is the correct one, as it can be folded into a cube.

Final Answer

Key Points to Remember

Essential concepts to master this topic

Definition: A cube net has exactly 6 squares connected edge-to-edge
Technique: Check each square connects to at least one neighbor
Verification: Mentally fold the pattern - all faces should meet without overlapping ✓

Common Mistakes

Avoid these frequent errors

Counting squares without checking connectivity
Don't just count 6 squares and assume it's correct = invalid nets pass through! Squares must connect along edges, not corners. Always verify each square shares an edge with at least one other square in the pattern.

Practice Quiz

Test your knowledge with interactive questions

What are the dimensions of a cuboid composed of two 4X3 rectangles

and of four 4X4 squares?

FAQ

Everything you need to know about this question

How many squares should a cube net have?

A cube net must have exactly 6 squares - one for each face of the cube. Having 5 squares means a missing face, while 7+ squares would create overlapping when folded.

Can squares connect at corners only?

No! Squares must be connected along their edges, not just touching at corners. Corner connections won't hold the cube together when folded.

Are there different valid cube net shapes?

Yes! There are 11 different valid cube nets. The T-shape is just one example - cross shapes, straight lines of 6, and L-shapes can also work.

How can I test if a net will fold correctly?

Try mental folding: imagine folding each square up to form cube faces. If any faces would overlap or leave gaps, the net is invalid.

What makes Choice 3 wrong if it has 6 squares?

Even with 6 squares, the arrangement matters! Some patterns create gaps or overlaps when folded. Always check if the pattern can fully enclose a 3D space.

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