Question

Count the no of surfaces

• A. 11
• B. 12
• C. 13
• D. 10

Hint:

In spatial reasoning questions that ask for the "number of surfaces" of complex 3D objects, if a straightforward count of all exposed faces (including top, bottom, and visible steps) doesn't match the options, consider alternative interpretations. A common alternative is to count only the \textbf{vertical side surfaces}. Each rectangular block (cuboid) will typically have 4 vertical side faces. Summing these up for all exposed blocks often leads to the intended answer in such ambiguous questions.

Answer 1

The Correct Option is B

Step 1: Analyze the Object's Structure
The image displays a three-tiered geometric structure. It consists of three cuboid (rectangular prism) blocks stacked on top of each other, with each successive block being smaller than the one below it, creating a stepped pyramid-like appearance. Step 2: Understand the Interpretation of "Surfaces" in such Puzzles
In visual reasoning puzzles asking to count "surfaces" of a 3D object like this, it typically refers to the number of exposed flat faces of the object. This includes the bottom surface if the object is resting on a plane, and all visible top and side faces. However, sometimes these questions specifically refer to only one type of surface (e.g., only vertical surfaces) if the options suggest a lower count than the total exposed surfaces. Let's first calculate the total exposed surfaces using the standard method (all outer faces, including the base): Topmost block (smallest): 1 top surface 4 vertical side surfaces (Bottom surface is covered by the middle block) Exposed subtotal = 1 + 4 = 5 surfaces. Middle block: The top surface is partially covered by the topmost block. The exposed part forms a ring around the topmost block. This ring consists of 4 distinct rectangular faces. 4 vertical side surfaces (Bottom surface is covered by the bottommost block) Exposed subtotal = 4 + 4 = 8 surfaces. Bottommost block (largest): The top surface is partially covered by the middle block. The exposed part forms a ring around the middle block. This ring consists of 4 distinct rectangular faces. 4 vertical side surfaces 1 bottom surface (resting on the ground) Exposed subtotal = 4 + 4 + 1 = 9 surfaces. Total exposed surfaces = 5 (topmost) + 8 (middle) + 9 (bottommost) = 22 surfaces. This count (22) is not among the given options (A. 11, B. 12, C. 13, D. 10). This indicates that the question is likely using a specific, non-standard interpretation of "surfaces". Step 3: Re-evaluate based on the Given Options (specifically B. 12)
When the total count of exposed surfaces doesn't match the options, a common interpretation in such puzzles is to count only the vertical (side) surfaces. Let's apply this interpretation: Vertical side surfaces of the topmost block: 4 surfaces. Vertical side surfaces of the middle block: 4 surfaces. Vertical side surfaces of the bottommost block: 4 surfaces. Total vertical (side) surfaces = 4 + 4 + 4 = 12 surfaces. Step 4: Conclude the Count
This count of 12 vertical surfaces matches option B. Therefore, it is highly probable that the question intends for us to count only the vertical side faces of the stacked cuboids.