CFAT Spatial Ability: 2D Unfolding 3 — Questions and Answers
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?
- Always the top face
- Always the bottom face
- Always a side face
- Any face, depending on orientation when folding (Correct answer)
Correct answer: Any face, depending on orientation when folding
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?
- A & D, B & C, E & F
- A & C, B & D, E & F (Correct answer)
- A & B, C & D, E & F
- A & F, B & E, C & D
Correct answer: A & C, B & D, E & F
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?
- Yes, if the squares are equal sized
- No, it is not a valid cube net (Correct answer)
- Yes, but only by bending along diagonals
- Yes, any 6-square arrangement folds into a cube
Correct answer: No, it is not a valid cube net
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?
- 5
- 6
- 7 (Correct answer)
- 8
Correct answer: 7
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?
- Identical in every way
- A mirror image (Correct answer)
- Rotated exactly 90 degrees
- Inside out with no visible faces
Correct answer: A mirror image
Flipping a net produces a mirror image because the inside and outside of each face are reversed.
Question 6: Which 3D shape has a net consisting of one rectangle and two circles?
- Sphere
- Cone
- Cylinder (Correct answer)
- Rectangular prism
Correct answer: Cylinder
A cylinder's net is one rectangle (the curved lateral surface unrolled flat) plus two circles (the top and bottom caps).
Question 7: A regular tetrahedron has 4 equilateral triangular faces. Its unfolded net contains:
- 3 triangles in a straight row only
- 4 triangles arranged as a strip or branching shape (Correct answer)
- 4 squares
- 3 triangles and 1 square
Correct answer: 4 triangles arranged as a strip or branching shape
A tetrahedron has exactly 4 triangular faces, so its net must contain all 4 triangles in a connected arrangement.
CFAT Spatial Ability: 2D Unfolding 3
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?