A solid wooden cube has its six faces marked with symbols: $\blacksquare$ (Top), $\bullet$ (Bottom), $\bigstar$ (Front), $\blacklozenge$ (Back), $\blacktriangle$ (Left), $\blacktriangledown$ (Right).
The cube is rotated $90^\circ$ clockwise about the vertical axis (viewed from above), and then rotated $90^\circ$ downward about the horizontal axis parallel to the front face (so the top face moves to the front). Which symbol is now visible on the FRONT face?
Options:
(A) $\blacktriangle$
(B) $\blacktriangledown$
(C) $\blacksquare$
(D) $\blacklozenge$
Answer Key:
C
Step-by-Step Solution & Explanation
**Method 1: Step-by-Step 3D Orientation Tracking**
- Initial orientation: $\text{Top} = \blacksquare, \text{Bottom} = \bullet, \text{Front} = \bigstar, \text{Back} = \blacklozenge, \text{Left} = \blacktriangle, \text{Right} = \blacktriangledown$.
1. First rotation: $90^\circ$ clockwise about the vertical axis (viewed from above). The vertical axis leaves the Top ($\blacksquare$) and Bottom ($\bullet$) unchanged. Front rotates to Left, Left rotates to Back, Back rotates to Right, and Right rotates to Front.
- Current Top remains $\blacksquare$.
2. Second rotation: $90^\circ$ downward about the horizontal axis (pitch forward). The Top face moves directly to the Front.
- Since the Top face remained $\blacksquare$ after the first rotation, it is now on the Front face.
Option **C** is correct.