GATE Civil 2022 Set 1 | GA Question: 10

Question

Consider a cube made by folding a single sheet of paper of appropriate shape. The interior faces of the cube are all blank. However, the exterior faces that are not visible in the above view may not be blank.

Which one of the following represents a possible unfolding of the cube?

     

       A.      

       B.      

       C.       

       D.         

 

Answer 1

Before solving the question, let’s first understand the rules of dice:

1. If there is one element that is common in both dices also having the same surface then the remaining surface of both dice is opposite to each other.

• Below are the opposite surfaces: 
  • $3 \longrightarrow 1$
  • $5 \longrightarrow 2$
  • $4 \longrightarrow 6$

2. If two numbers are the same in both dices whether their surface is not equal, then the remaining number of both dice are opposite to each other.

• Below are the opposite surfaces:  
  • $5 \longrightarrow 2$

3. If there is one element common in both the dices having different surfaces then rotate it in the clockwise direction to find out the opposite surface.

 

• Below are the opposite surfaces: 
  • $5 \longrightarrow 1$
  • $4 \longrightarrow 6$
• $\textbf{Note:}$ After rotating in a clockwise direction  $6 \& 4$ become the first appearance So these are opposite to each other. $5 \& 1$ appear in the second one So, these ones are opposite each other.

4. The opposite surface of the open dice can be find by the below method:
   1. Alternate surfaces are opposite to each other.
   2. No two opposite surfaces are touched by side or by a corner 

• Below are the opposite surfaces: 
  • $\text{M} \longrightarrow \text{Q}$
  • $\text{N} \longrightarrow \text{R}$
  • $\text{T} \longrightarrow \text{S}$

Now, let's solve the question.

Given original figure:

The black edge is perpendicular to the given line and the white shaded edge is parallel to the given line.

So, only option $\text{(D)}$ is possible.

Correct Answer $:\text{D}$