Question

Visualize a cube that is held with one of the four body diagonals aligned to the vertical axis. Rotate the cube about this axis such that its view remains unchanged. The magnitude of the minimum angle of rotation is:

• A. \( 120^\circ \)
• B. \( 60^\circ \)
• C. \( 90^\circ \)
• D. \( 180^\circ \)

Hint:

For symmetry-related questions, analyze the structure's rotational order and divide \( 360^\circ \) by the number of symmetric positions.

Answer 1

The Correct Option is A

Step 1: Understanding the symmetry of a cube. A cube has rotational symmetry about its body diagonal. Rotating the cube about this diagonal such that its view remains unchanged corresponds to the angle of rotation matching the symmetry of the cube. Step 2: Calculating the rotation angle. The body diagonal rotation symmetry of a cube divides \( 360^\circ \) into three equal rotations: \[ {Minimum angle of rotation} = \frac{360^\circ}{3} = 120^\circ. \] Step 3: Conclusion. The minimum angle of rotation is \( {(1)} 120^\circ \).