Spatial Reasoning Practice Questions
A sheet of paper has been folded. How will it appear when opened?
Answer Figures:
To solve this problem, we need to follow the paper folding process shown in the figure and determine how it will appear when unfolded.
In the first step, the paper has a diagonal line from the top-left to bottom-right. This represents the fold line.
After the folding steps are completed and the paper is opened, the triangular shape will have a clear crease along the original fold line, which matches option (1).
Option (2) shows an additional vertical crease which is not created in the folding process shown.
Option (3) shows a dotted line that doesn’t match the fold pattern.
Option (4) shows a small line segment that doesn’t correspond to any fold in the original sequence.
Therefore, option B (figure 1) is the correct answer.
How many triangles are in the figure?
To solve this problem, we need to systematically count all triangles in the figure.
The figure is a hexagon with three internal lines creating triangular regions. Let’s count them methodically:
- The six small triangles formed around the perimeter of the hexagon: 6 triangles
- The four triangles formed by the intersection of the internal lines: 4 triangles
Total: 6 + 4 = 10 triangles
Here’s a breakdown of the triangles:
- Small triangles: top-left, top-right, middle-left, middle-right, bottom-left, bottom-right
- Internal triangles: upper central, lower central, left central, right central
Therefore, option C (10 triangles) is the correct answer.
Which of the following nets will form a cube when folded?
To solve this problem, we need to check if each net contains exactly 6 squares and can be folded to form a cube without any overlap.
Net A: This is a T-shape with 5 squares. A cube needs 6 faces, so this net is missing one square and cannot form a complete cube.
Net B: This is a cross shape with 6 squares. When folded, each square will form one face of the cube with no overlaps, forming a complete cube.
Net C: This is a line of 6 squares. When trying to fold this, squares would overlap and it could not form a cube. A cube cannot be formed from a straight line of squares because they would need to fold in multiple directions.
Net D: This has 6 squares in an L-shape with an extension. However, when trying to fold this shape, some squares would overlap or leave gaps, making it impossible to form a perfect cube.
Therefore, only option B (the cross shape) can be folded to form a complete cube, making the answer “B only”.
Which figure completes the pattern?
To solve this problem, we need to identify the pattern in the sequence and determine which option continues it logically.
Looking at the sequence:
- First figure: Two concentric circles
- Second figure: Two concentric circles with a vertical line
- Third figure: Two concentric circles with a vertical and horizontal line (forming a plus sign)
The pattern shows the progressive addition of lines in specific orientations:
- Start with concentric circles
- Add a vertical line
- Add a horizontal line
- The next logical step would be to add a diagonal line
Option A shows the two concentric circles with a vertical line, horizontal line, and one diagonal line (from top-left to bottom-right), which follows the pattern of adding one new line at each step.
Option B adds two diagonal lines at once, which doesn’t follow the established pattern of adding one line at a time.
Option C is missing the inner circle, which breaks the pattern.
Option D is missing both the vertical and horizontal lines that were already established in the sequence.
Therefore, option A is the correct answer as it follows the logical progression of the pattern.
Which of the options shows the correct rotation of the 3D object below?
After rotating 90° clockwise around the vertical axis:
To solve this problem, we need to visualize how the object would look after a 90° clockwise rotation around the vertical axis.
The original object is an L-shaped 3D figure. When rotated 90° clockwise around the vertical axis:
- The front face would move to the right side
- The right side would move to the back
- The back would move to the left side
- The left side would move to the front
- The top and bottom faces remain in the same orientation (though their shapes might appear different from our viewpoint)
Looking at option B:
- The L-shape has been correctly rotated so that what was previously extending to the right now extends toward the back (from our viewpoint)
- The proportions and connections between different faces are maintained correctly
- The visible faces are consistent with what would be visible after the described rotation
Options A, C, and D show incorrect rotations, with either wrong orientations of the L-shape or incorrect connections between faces.
Therefore, option B is the correct answer as it accurately represents the object after a 90° clockwise rotation around the vertical axis.
Practice Makes Perfect!
Spatial reasoning is a skill that improves with practice. Regular exercise of your spatial visualization abilities can enhance your performance in fields like architecture, engineering, mathematics, and many scientific disciplines.