Question

The paper as shown in the figure is folded to make a cube where each square corresponds to a particular face of the cube. Which one of the following options correctly represents the cube? \textit{Note: The figures shown are representative.} \begin{center} \includegraphics[width=0.7\textwidth]{01.jpeg} \end{center}

• A. A
• B. B
• C. C
• D. D

Hint:

When solving cube-net folding questions, always check which faces are \emph{adjacent} in the net. Opposite faces can never appear next to each other in the folded cube.

Answer 1

The Correct Option is B

Step 1: Analyze the unfolded cube net.
The given net consists of: - Center square with $\triangle$ (hollow triangle). - Left square blank. - Right square with $\blacktriangle$ (filled triangle). - Top square with $\bullet$ (solid dot). - Bottom square with $\bigcirc$ (hollow circle). \bigskip Step 2: Visualize folding.
- The central $\triangle$ face becomes the \emph{front} of the cube. - The $\blacktriangle$ (right face in the net) will fold to become the \emph{right} face of the cube. - The $\bullet$ (top) will fold onto the \emph{top} face of the cube. - The $\bigcirc$ (bottom) folds to the \emph{bottom} face. - The left blank square becomes the \emph{left} face. \bigskip Step 3: Check adjacency.
- The $\triangle$ (front) must be adjacent to $\blacktriangle$ (right), $\bullet$ (top), $\bigcirc$ (bottom), and the blank (left). - Opposite faces are: - $\bullet$ (top) opposite $\bigcirc$ (bottom). - $\triangle$ (front) opposite the blank face (left). \bigskip Step 4: Match with given options.
- (A) $\triangle$ with $\bullet$ on top → Wrong, because $\bullet$ is opposite $\bigcirc$, not necessarily directly visible along with $\triangle$ in this configuration.
- (B) $\triangle$ front, $\blacktriangle$ right → Correct, because these two are adjacent in the net and fold correctly.
- (C) $\triangle$ front, blank right → Incorrect, blank is opposite $\triangle$, not on the side.
- (D) $\triangle$ front, $\blacktriangle$ top, $\bullet$ side → Impossible, since $\blacktriangle$ is not on the top face. \bigskip Step 5: Conclusion.
The only consistent cube representation is option (B). \[ \boxed{\text{Correct representation: Option (B)}} \] \bigskip