A paper shown in Panel I is folded along the dashed lines (- - -) to construct a cube. The shaded regions shown in Panel I appear on the outer surface of the cube. Referring to cubes shown in Panel II, which one of the options is correct?

Question

Which one of the following gases is primarily responsible for the formation of photochemical smog?

Answer 1

A more systematic way to solve cube-net problems is to assign face labels algebraically instead of visualising the fold directly.

Let the central square of the net be $F$ (front). Moving outward along the vertical strip of four squares, the square above $F$ becomes $U$ (up/top), the square below $F$ becomes $D$ (down/bottom), and the square attached beyond $D$ becomes $K$ (back), since a strip of four squares folds through the cycle $F \to U \to K \to D \to F$ as it wraps around the cube. The two squares attached to the left and right of $F$ become $L$ and $R$ directly, with no cycling needed.

Every crease in the net corresponds to a shared edge between two of these six labels, and the golden rule of such problems is: $F$ is adjacent to $U, D, L, R$ but never to $K$; and $U$ is never adjacent to $D$, and $L$ is never adjacent to $R$, since these are always the three pairs of opposite faces on any cube.

Now check each candidate drawing by naming its three visible faces using this label system and testing two things: (a) are the three faces mutually adjacent (i.e. no two of them are an opposite pair), and (b) does the shading at every shared edge continue in the same, non-reversed direction implied by the net.

Carrying this test out shows cube (i) requires one face's pattern to appear reversed relative to its neighbours, which is impossible for a single folded sheet, while cube (ii) satisfies both conditions cleanly.

\[\boxed{\text{Only cube (ii) is a valid fold of the net, Option 2}}\]

Answer 2

A more systematic way to solve cube-net problems is to assign face labels algebraically instead of visualising the fold directly.

Let the central square of the net be $F$ (front). Moving outward along the vertical strip of four squares, the square above $F$ becomes $U$ (up/top), the square below $F$ becomes $D$ (down/bottom), and the square attached beyond $D$ becomes $K$ (back), since a strip of four squares folds through the cycle $F \to U \to K \to D \to F$ as it wraps around the cube. The two squares attached to the left and right of $F$ become $L$ and $R$ directly, with no cycling needed.

Every crease in the net corresponds to a shared edge between two of these six labels, and the golden rule of such problems is: $F$ is adjacent to $U, D, L, R$ but never to $K$; and $U$ is never adjacent to $D$, and $L$ is never adjacent to $R$, since these are always the three pairs of opposite faces on any cube.

Now check each candidate drawing by naming its three visible faces using this label system and testing two things: (a) are the three faces mutually adjacent (i.e. no two of them are an opposite pair), and (b) does the shading at every shared edge continue in the same, non-reversed direction implied by the net.

Carrying this test out shows cube (i) requires one face's pattern to appear reversed relative to its neighbours, which is impossible for a single folded sheet, while cube (ii) satisfies both conditions cleanly.

\[\boxed{\text{Only cube (ii) is a valid fold of the net, Option 2}}\]

A paper shown in Panel I is folded along the dashed lines (- - -) to construct a cube. The shaded regions shown in Panel I appear on the outer surface of the cube. Referring to cubes shown in Panel II, which one of the options is correct?

Show Hint

The Correct Option is B

Solution and Explanation

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