A solid object under a spotlight forms a shadow as shown in the image. Which of the options can be produced by rotating the object?
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In shadow projection problems, consider the views from all six principal axes (top, bottom, front, back, left, right). Remember that a 3D object can have very different 2D silhouettes depending on the viewing angle. Simple-looking objects can create complex shadows and vice-versa.
Option A: Viewed from a corner angle, the arms of the cross-shaped solid overlap each other and the outline reduces to a bent L shape, so this is possible.
Option B: A rigid solid's shadow always has a clean, describable outline at every angle; a vague irregular blob does not match any single rotation of this object, so this is not possible.
Option C: Viewed face on along its main axis, the object casts its full four-armed plus shape, so this is possible.
Option D: Viewed edge on, the arms line up behind one another and only a long bar is visible, so this is possible.
The object can produce A, C, and D, but not B.
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Approach Solution -2
A cleaner way to approach this is to eliminate first: find the one outline that could never come from rotating a single rigid solid, then confirm the rest fit as different viewing angles of that same solid.
Option B: Every genuine rotation of a rigid solid produces a shadow with straight, well-defined edges determined by the object's faces — there is no rotation that turns a blocky solid into a vaguely irregular outline with no clear structure. This option is eliminated first.
Option C: With that ruled out, the plus outline is simply the object's home view, seen straight on, so it is valid.
Option D: Rotating 90 degrees to look along one arm collapses the branches into a single strip, giving the bar outline, so it is valid.
Option A: Rotating to an in-between, oblique angle makes some arms overlap in projection while one remains extended, producing the bent L outline, so it is valid.
Once the irregular outline is eliminated, the remaining three all check out as valid rotations.
