CFAT Spatial Ability: 2D Unfolding 3

Question 1

In a cube net shaped like a cross (one center square with four squares extending outward), the center square will become which face when folded?

Accepted Answer

Any face, depending on orientation when folding

Answer

The center square of a cross net can become any face of the cube depending on how you orient it before folding.

Question 2

A cube net has square E above square A, then A-B-C-D in a row, then square F below square C. Which squares become opposite faces when folded?

Accepted Answer

A & C, B & D, E & F

Answer

Wrapping A-B-C-D around forms four sides: A(front) opposite C(back), B(right) opposite D(left), and E(top) opposite F(bottom).

Question 3

A 2×3 rectangular grid of 6 equal squares is cut out. Can it be folded into a cube?

Accepted Answer

No, it is not a valid cube net

Answer

A 2×3 rectangular grid cannot fold into a cube because opposite faces would overlap during folding.

Question 4

To create a flat net from a cube by cutting edges, how many of the cube's 12 edges must be cut?

Accepted Answer

7

Answer

Cutting 7 of the 12 edges leaves 5 edges as hinges, forming a connected spanning tree of all 6 faces.

Question 5

A cube net is flipped over (turned face-down). When folded, how does the resulting cube compare to folding it face-up?

Accepted Answer

A mirror image

Answer

Flipping a net produces a mirror image because the inside and outside of each face are reversed.

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