下列哪一个是正方体的展开图?

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完整解法

10

1. Analyse Diagram (1) by mentally folding it.

Let the middle square of the central row be the base.

  • The left and right squares fold up to form the left and right faces.
  • The square below folds up to form the front face.
  • The two squares above are attached to the left and right faces. When folded, both will swing to the top, overlapping each other to form the top face, leaving the back face empty.
  • Thus, (1) is not a valid net.

2. Analyse Diagram (2) by mentally folding it.

Let the bottom square of the left column be the base.

  • The middle square folds up to form the back face, and the top square folds over to form the top face.
  • The first square of the horizontal row folds up to form the right face.
  • The second square of the horizontal row folds to form the front face.
  • The single square attached to the bottom of the front face will fold to the bottom, overlapping with the base.
  • Thus, (2) is not a valid net.

3. Analyse Diagram (3) by mentally folding it.

Let the middle square of the vertical column be the base.

  • The top square folds up to form the back face. The square attached to its left folds to form the left face.
  • The bottom square folds up to form the front face.
  • The square attached to its right folds to form the right face.
  • The last square extending downwards from the right face will fold over to form the top face.
  • All 6 faces are uniquely covered without any overlaps. Thus, (3) is a valid net of a cube.
答案

Option (3)

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