Math Problem Statement

Which cube can be folded out of this net?

Solution

The puzzle you’ve provided is a classic "cube net" problem, where you need to determine which 3D cube can be folded from the 2D net shown. Here's how to approach this:

  1. Examine the Net: The net has six faces in the following colors:

    • Top left: Black
    • Bottom left: Yellow
    • Middle left: Green
    • Middle right: Red
    • Bottom right: Blue
    • Top right: Purple
  2. Matching Sides in the Cube: A key insight is that opposite sides of the cube must never touch. The six faces in the net must form adjacent pairs correctly when folded into a cube.

  3. Analyze Cube Options:

    • Cube A: Shows black adjacent to red, which is correct based on the net.
    • Cube B: Shows yellow adjacent to blue, which is incorrect based on the net since yellow and blue are on opposite sides.
    • Cube C: Shows black adjacent to green, but black should be adjacent to red or purple instead.
    • Cube D: Shows black adjacent to red and yellow, which fits.
    • Cube E: Shows black adjacent to green, which is incorrect.
    • Cube F: Shows yellow adjacent to blue, which is incorrect since these are opposite sides.

Conclusion: Cube A can be folded from this net.

Would you like further clarification on any step? Here are five related questions to extend this topic:

  1. How many distinct nets are possible for a cube?
  2. What are some common strategies to solve cube net problems?
  3. Can a cube net ever have fewer than 6 faces?
  4. How can 3D visualization skills improve spatial reasoning for these puzzles?
  5. How do cube nets relate to geometry in higher dimensions?

Tip: Always check which faces are opposite in a net to eliminate wrong options quickly.

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Math Problem Analysis

Mathematical Concepts

Spatial reasoning
3D geometry
Nets of cubes

Formulas

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Theorems

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Suitable Grade Level

Grades 6-8