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Which net could be folded into a cube?(1 point)

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An illustration shows the unfolded version of an object comprising of 6 squares. There are 3 adjoining squares positioned horizontally. The first square shares its bottom side with an adjoining fourth square. The third horizontal square shares its bottom side with a fifth square and a sixth square that are stacked vertically. Folds are shown as dashed lines.
Image with alt text: An illustration shows the unfolded version of an object comprising of 6 squares. There are 3 adjoining squares positioned horizontally. The first square shares its bottom side with an adjoining fourth square. The third horizontal square shares its bottom side with a fifth square and a sixth square that are stacked vertically. Folds are shown as dashed lines.

An illustration shows the unfolded version of an object comprising of 6 squares. There are three rows of squares. The first row is a single square. The second row is 2 squares. The second square of the second row adjoins the bottom of the square in the first row. The third row is 3 squares. The first square of the third row adjoins the bottom of the second square of the second row. Folds are shown as dashed lines.
Image with alt text: An illustration shows the unfolded version of an object comprising of 6 squares. There are three rows of squares. The first row is a single square. The second row is 2 squares. The second square of the second row adjoins the bottom of the square in the first row. The third row is 3 squares. The first square of the third row adjoins the bottom of the second square of the second row. Folds are shown as dashed lines.

An illustration shows the unfolded version of an object comprising of 6 squares. There are three adjoining squares positioned horizontally. The first square shares its top side with an adjoining square. The second square shares its bottom side with an adjoining square. The third square shares its top side with an adjoining square. Folds are shown as dashed lines.
Image with alt text: An illustration shows the unfolded version of an object comprising of 6 squares. There are three adjoining squares positioned horizontally. The first square shares its top side with an adjoining square. The second square shares its bottom side with an adjoining square. The third square shares its top side with an adjoining square. Folds are shown as dashed lines.

An illustration shows an unfolded version of a cube. Four adjoining squares are positioned horizontally. A fifth square adjoins the top side of the first square. A sixth square adjoins the bottom side of the fourth square. Folds are shown as dashed lines.

1 answer

To determine which net can be folded into a cube, we need to analyze the configurations of the nets provided. A valid net for a cube must have six squares arranged such that every square can be connected to fold into the cube's six faces.

  1. Net 1: The net has 6 squares arranged in a 'T' configuration, which allows for all squares to be folded around the edges of the cube. This can form a cube.

  2. Net 2: This configuration has squares in multiple rows that lead to an arrangement where some squares will not connect properly to form a cube. This cannot form a cube.

  3. Net 3: The three squares positioned horizontally with adjoining squares above and below also do not connect properly to create the sides necessary for a cube. This cannot form a cube.

  4. Net 4: This net has four squares in a line with two additional squares on top and bottom. However, this would not correctly fold into a cube as all faces cannot connect adequately. This cannot form a cube.

From this analysis, Net 1 is the only net that can be folded into a cube.