CFAT Spatial Ability: 3D Folding 2 — Questions and Answers
Question 1: A cube has 6 faces. When any valid net of a cube is folded, how many pairs of opposite faces does the finished cube always have?
- 1 pair
- 2 pairs
- 3 pairs (Correct answer)
- 4 pairs
Correct answer: 3 pairs
Every cube has exactly 3 pairs of opposite faces, one pair for each spatial axis (top/bottom, front/back, left/right).
Question 2: In a cube net, square A shares an edge with square B. After folding the net into a cube, squares A and B will be:
- Opposite faces
- Adjacent faces sharing an edge (Correct answer)
- Adjacent faces sharing only a vertex
- Non-touching faces
Correct answer: Adjacent faces sharing an edge
Squares that share an edge in the net will also share an edge in the finished cube — the fold line becomes the shared edge.
Question 3: A cube net is laid flat. Two squares that are NOT directly connected to each other in the net will become what in the folded cube?
- Definitely opposite faces
- Definitely adjacent faces
- Either adjacent or opposite, depending on their positions (Correct answer)
- Never-touching faces
Correct answer: Either adjacent or opposite, depending on their positions
Non-adjacent squares in the net can become either opposite or adjacent faces depending on their specific layout — position in the net determines this.
Question 4: How many distinct flat arrangements (hexominoes) of 6 squares can be folded into a valid cube?
- 8
- 9
- 11 (Correct answer)
- 14
Correct answer: 11
There are exactly 11 distinct hexominoes that can be folded into a cube — a proven geometric result.
Question 5: A rectangular prism (box) has three different pairs of faces: top/bottom, front/back, and left/right. Its net laid flat will always contain how many total rectangles?
- 4
- 5
- 6 (Correct answer)
- 8
Correct answer: 6
A rectangular prism has exactly 6 faces (3 pairs of opposite rectangles), so its net always contains 6 rectangles.
Question 6: A cube has 12 edges. When it is unfolded into a flat net by cutting along some edges, how many edges must be cut to produce a valid net?
- 5
- 6
- 7 (Correct answer)
- 8
Correct answer: 7
To keep all 6 squares connected as a flat tree, 5 edges remain as fold lines and 7 of the 12 edges are cut.
Question 7: A cube net is reflected in a mirror. When the mirror-image net is folded into a cube, the result compared to the original cube is:
- An identical cube in every way
- A mirror-image cube (chirality reversed) (Correct answer)
- A cube with different dimensions
- An invalid shape that cannot close properly
Correct answer: A mirror-image cube (chirality reversed)
Reflecting a cube net reverses chirality, producing a mirror-image cube — same size and shape but with faces oriented oppositely.
CFAT Spatial Ability: 3D Folding 2
A cube has 6 faces.
When any valid net of a cube is folded, how many pairs of opposite faces does the finished cube always have?