CFAT - Canadian Forces Aptitude Spatial Ability: 2D Unfolding Questions and Answers 1 — Questions and Answers
Question 1: Which of the following 3D shapes can be formed from the 2D pattern shown? (Image depicts a 2D net of a cube with symbols: a solid black circle, a hollow square, and an 'X' on adjacent faces in a line. The face with the 'X' is in the center.)
- A cube where the 'X' and the solid circle share an edge, and the hollow square is opposite the 'X'.
- A cube where the solid circle and the hollow square are on opposite faces.
- A cube where the 'X', the solid circle, and the hollow square all meet at a single vertex. (Correct answer)
- A cube where the 'X' is on top, and the solid circle is on the bottom face.
Correct answer: A cube where the 'X', the solid circle, and the hollow square all meet at a single vertex.
When the 2D pattern is folded, the face with the solid circle and the face with the hollow square will be adjacent to the central 'X' face. If you imagine folding the pattern up, the circle, 'X', and square faces will all wrap around and meet at one corner (vertex). The faces opposite each other would be the circle and the blank face to its right, the 'X' and the blank face below it, and the square and the blank face at the end of the line.
Question 2: A soldier needs to assemble a box from a flat piece of cardboard. The pattern is a standard six-square cross shape for a cube. If the bottom-most square in the vertical part of the cross is the base of the cube, which square becomes the top lid?
- The square to the left of the vertical column.
- The second square from the bottom in the vertical column.
- The square to the right of the vertical column.
- The top-most square in the vertical column. (Correct answer)
Correct answer: The top-most square in the vertical column.
In a standard cross-shaped net (four squares in a vertical line and one on each side of the second square from the top), if you designate the bottom square as the base, the three squares above it will fold up to form the front, top, and back sides in sequence. Therefore, the top-most square folds over to become the lid.
Question 3: Examine the provided 2D net. Which of the answer choices represents the correct 3D object when the net is folded? (Image shows a net with a central rectangular face, with two smaller square faces attached to its shorter sides, and two triangular faces attached to its longer sides.)
- A cube
- A triangular prism (Correct answer)
- A square pyramid
- A cylinder
Correct answer: A triangular prism
The provided net consists of three rectangular/square faces and two triangular faces. When folded, the two triangular faces form the ends, and the three rectangular/square faces form the sides. This configuration creates a triangular prism.
Question 4: If the 2D pattern is folded to form a cube, which face will be opposite the face with the star?
- The face with the triangle
- The face with the circle
- The face with the square (Correct answer)
- The blank face
Correct answer: The face with the square
In this standard 'T' shaped net, faces that are separated by one other face will be opposite each other when folded. Following this rule, the star is separated from the square by the circle. Therefore, the star and the square will be on opposite sides of the cube.
Question 5: A 2D pattern is made of six squares in a single row. What happens when you try to fold this pattern to create a cube?
- It forms a cube with one open side.
- It forms a complete and closed cube.
- It forms an open-ended rectangular tube, but not a cube.
- It is impossible to form a closed 3D shape because the faces will overlap. (Correct answer)
Correct answer: It is impossible to form a closed 3D shape because the faces will overlap.
A net for a closed cube requires the six squares to be arranged so they can enclose a volume without overlapping. When six squares are arranged in a single 1x6 row, folding them will cause the fifth and sixth squares to overlap the first and second squares, respectively, preventing the formation of a closed cube.
Question 6: You are given a 2D pattern to fold into the 3D shape shown. Which corner of the pattern, labeled 1, 2, 3, or 4, will touch the corner marked with an 'X' on the folded cube? (Image shows a 2D net and a corresponding 3D cube. The net is a cross shape. The central square has an 'X' in one corner. The surrounding squares have corners labeled 1, 2, 3, 4.)
- Corner 2 (Correct answer)
- Corner 4
- Corner 1
- Corner 3
Correct answer: Corner 2
When the pattern is folded, the faces attached to the central square fold up. By tracing the connections, corner 2 from the top flap, a corner from the left flap, and the 'X' corner from the central flap all converge to form a single vertex on the final cube. Therefore, corner 2 will touch corner 'X'.
CFAT - Canadian Forces Aptitude Spatial Ability: 2D Unfolding Questions and Answers 1
Which of the following 3D shapes can be formed from the 2D pattern shown? (Image depicts a 2D net of a cube with symbols: a solid black circle, a hollow square, and an 'X' on adjacent faces in a line.
The face with the 'X' is in the center.)