Math Problem Statement

Which cube can be folded from this 2D net?

Solution

To solve the problem in the image and identify which 3D cube can be formed from the given 2D net, we need to analyze the arrangement of the faces.

Steps to analyze:

  1. Understand the net: The 2D net has six faces that are folded to form the cube. The key faces are numbered by their dots.

  2. Observe opposite faces:

    • In a standard die, opposite faces always add up to 7. For example:
      • 1 is opposite to 6.
      • 2 is opposite to 5.
      • 3 is opposite to 4.
  3. Visualize the fold:

    • When folding the 2D net, adjacent faces will be next to each other on the cube.
    • You need to mentally fold the 2D net and check which cube from the given options follows this configuration.

Solution:

  • From the net, it seems that:
    • The face with 5 dots is adjacent to 3, 1, and 4 dots.
    • Therefore, the face with 2 dots will be opposite the 5 dots face.
    • Following this logic, cube number 2 matches the configuration correctly when the net is folded.

Would you like more details or have questions about any part of this explanation?

Here are 5 related questions you might find interesting:

  1. What are the common configurations for standard dice faces?
  2. How do opposite faces of a cube affect folding in geometry?
  3. Can any 2D net be folded into a cube? Why or why not?
  4. How can symmetry help in visualizing 3D shapes from 2D nets?
  5. What other polyhedra can be formed using a similar net-folding technique?

Tip: When working with 2D nets, always check how adjacent faces interact when folded to help visualize the 3D shape.

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Math Problem Analysis

Mathematical Concepts

Geometry
3D Shapes
Spatial Visualization

Formulas

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Theorems

Opposite Faces Theorem on Standard Cubes

Suitable Grade Level

Grades 6-8