CFAT - Canadian Forces Aptitude Spatial Ability: 3D Folding Questions and Answers 1 — Questions and Answers
Question 1: A 2D pattern for a cube is shown. Three of the answer choices are possible views of the cube when it is folded. Which view is IMPOSSIBLE to create from the given pattern? The pattern is a cross shape: the central square has a plus sign (+). The square above it has a solid circle. The square below it has a solid triangle. The square to the left is blank. The square to the right has three horizontal lines. The square below the triangle has a hollow square.
- A view showing the solid circle, the plus sign, and the blank face.
- A view showing the plus sign, the hollow square, and the three horizontal lines.
- A view showing the solid triangle, the hollow square, and the blank face. (Correct answer)
- A view showing the solid triangle, the plus sign, and the blank face.
Correct answer: A view showing the solid triangle, the hollow square, and the blank face.
In the given 2D net, the solid triangle and the hollow square are on opposite ends of the main vertical column, separated by the plus sign. When folded, faces that are opposite on the net cannot be visible at the same time. The view described in the correct answer shows the solid triangle and the hollow square simultaneously, which is impossible.
Question 2: The provided 2D net is folded to form a cube. Which face will be adjacent to BOTH the face with the star and the face with the arrow? The net is a cross shape: the central square is blank. The square above it is a star. The square below it is a circle. The square to the left is an arrow pointing left. The square to the right is a diamond. The square at the very top of the pattern (attached to the star) is a square.
- The face with the square (Correct answer)
- The face with the diamond
- The blank face
- The face with the circle
Correct answer: The face with the square
If you visualize folding the net with the blank face as the front, the star becomes the top face and the arrow becomes the left face. The 'square' face then folds over from the top to become the back face. The back face is adjacent to the top (star), bottom, left (arrow), and right sides. Therefore, the 'square' face is adjacent to both the star and the arrow.
Question 3: A technician is fabricating a part from a flat sheet of metal. The 2D pattern consists of one central hexagonal face with a triangle attached to each of its six sides. When this pattern is correctly folded, what 3D shape is created?
- Hexagonal Prism
- Octahedron
- Dodecahedron
- Hexagonal Pyramid (Correct answer)
Correct answer: Hexagonal Pyramid
The pattern has a single hexagonal face, which serves as the base of the shape. The six triangular faces fold upward, and their vertices meet at a single point (an apex) above the base. This construction forms a hexagonal pyramid.
Question 4: The image displays a folded cube showing three faces. The front face has a vertical line (|), the top face has a horizontal line (—), and the right-side face has a circle (O). Which of the following 2D nets could be folded to create this specific cube?
- A net where the circle and vertical line are on opposite sides of the horizontal line's face.
- A cross-shaped net with the vertical line in the center, the horizontal line above it, and the circle to its right. (Correct answer)
- A net with the three symbols in a single row in the order: circle, vertical line, horizontal line.
- A cross-shaped net with the vertical line in the center, the horizontal line below it, and the circle to its left.
Correct answer: A cross-shaped net with the vertical line in the center, the horizontal line above it, and the circle to its right.
To match the cube, the three faces must meet at a single corner. In the correct net, if you designate the face with the vertical line as the front, the face above it (with the horizontal line) will fold to become the top, and the face to its right (with the circle) will fold to become the right side. This arrangement perfectly matches the cube shown.
Question 5: The 2D net shown is folded into a cube. Based on the net's layout, which symbol is on the face opposite the face with the diamond? The net is T-shaped. The vertical part has four squares (from top to bottom): star, plus, circle, square. The horizontal part consists of a diamond to the left of the 'plus' face and an arrow to the right of the 'plus' face.
- Plus
- Arrow (Correct answer)
- Star
- Circle
Correct answer: Arrow
When this T-shaped net is folded, the 'diamond' and the 'arrow' are on opposite sides of the central 'plus' face. If you imagine the 'plus' face as the front of the cube, the 'diamond' folds to become the left face, and the 'arrow' folds to become the right face, making them directly opposite each other.
Question 6: A line is drawn on the 2D pattern of a cube as shown. The pattern is a cross shape. A straight line starts at the midpoint of the left edge of the central square, passes through its center, and ends at the midpoint of its right edge. A second straight line is on the square to the right of the central square; it runs from the midpoint of its left edge to its center. Which option shows the resulting line on the folded cube?
- A continuous 'T' shape across two faces.
- Two separate, unjoined lines on adjacent faces.
- A continuous straight line that crosses from the front face to the right-side face, ending at the center of the right-side face. (Correct answer)
- A continuous line that forms a right angle at the edge between two faces.
Correct answer: A continuous straight line that crosses from the front face to the right-side face, ending at the center of the right-side face.
The line on the central square crosses it completely from the left edge to the right edge. The line on the right-hand square starts at its left edge (which it shares with the central square's right edge) and goes to its center. When folded, the right edge of the central square joins with the left edge of the right-hand square. The two lines will meet at this edge and form a single, continuous straight line that starts at the center of the left face, crosses the entire front face, and continues to the center of the right face.
