Question

From a 3-dimensional structure made of cubes, eight rows of cubes have been removed as shown below. Select the correct pattern that will emerge from the side shown with an arrow. 

• A. A
• B. B
• C. C
• D. D

Hint:

For 3D to 2D projection problems, be systematic. Go slice by slice or column by column. Use a piece of paper to track the pattern as you build it to avoid confusion.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept: 
This is a 3D visualization problem. We need to determine the 2D side view (an orthographic projection) of a 3D object from a specified direction. Black squares in the options represent a cube being present at that position, and white squares represent a missing cube. 
Step 2: Key Formula or Approach: 
The approach is to analyze the 3D structure column by column, from left to right, as seen from the direction of the arrow. For each column, we determine which cubes are present in the four vertical levels (rows). 
Step 3: Detailed Explanation: 
The structure is 4 cubes high and appears to be 8 cubes wide from the arrow's perspective. Let's map the visible cubes for each vertical column from left to right (C1 to C8). 'B' means black (cube present), 'W' means white (cube absent). We list the rows from top to bottom (R1 to R4). 
Column 1: No cubes are removed. The column is full. Pattern: B, B, B, B. 
Column 2: The second row from the top is removed. Pattern: B, W, B, B. 
Column 3: The first row from the top is removed. Pattern: W, B, B, B. 
Column 4: The third row from the top is removed. Pattern: B, B, W, B. 
Column 5: The fourth row from the top (bottom row) is removed. Pattern: B, B, B, W. 
Column 6: The pattern repeats. The hole is in the second row from the top. Pattern: B, W, B, B. 
Column 7: The hole is in the first row from the top. Pattern: W, B, B, B. 
Column 8: This is the end column, which is full. Pattern: B, B, B, B. 
Step 4: Comparing with Options: 
Now, let's assemble this pattern and compare it with the given options. The resulting pattern is: 
Col 1: All black 
Col 2: White in Row 2 
Col 3: White in Row 1 
Col 4: White in Row 3 
Col 5: White in Row 4 
Col 6: White in Row 2 
Col 7: White in Row 1 
Col 8: All black 
This exact pattern matches option (A). Options (B), (C), and (D) show different arrangements of the missing cubes. 
Step 5: Final Answer: 
The correct pattern that emerges from the side view is option (A).