In Panel I of the figure below, the front view and top view of a structure are shown. Which one of the 3D structures shown in Panel II possesses the views shown in Panel I?
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Match the footprint (top view) first to eliminate solids with extra or missing cubes, then check the height profile (front view) of the remaining candidates.
Step 1: Understand what a front view and a top view represent. A front view is the silhouette a solid casts when viewed straight on (looking along the depth axis), and it records the height profile of the object column by column. A top view is the silhouette seen looking straight down, and it records the footprint (the ground plan) of the object, cell by cell.
Step 2: Read off the shape from Panel I. Panel I shows a front view that is a two level stepped outline (an L shaped stack of unit cubes, taller on one side and shorter on the other), and a top view that is likewise an irregular stepped footprint of unit squares, not a full rectangle. Both views therefore rule out any option whose front or top silhouette is a solid rectangular block, and they rule out any option whose top view footprint has more or fewer occupied cells than Panel I.
Step 3: Compare each candidate solid in Panel II against these two silhouettes. For each of the four solids (i), (ii), (iii), (iv), project it from the front and from the top and match the resulting outline against Panel I. Structures (ii), (iii) and (iv) each show at least one mismatch: either an extra cube appears in the top view footprint that is not present in Panel I, or the front view step pattern (the sequence of column heights) does not line up with the two step heights shown in Panel I.
Step 4: Confirm the match. Structure (i) is the only solid whose front view reproduces the exact stepped two tier outline of Panel I's front view, and whose top view reproduces the exact irregular footprint of Panel I's top view, with no extra or missing unit cubes in either projection.
Step 5: Eliminate the remaining options. Options (B), (C) and (D) correspond to structures (ii), (iii) and (iv), each of which fails to reproduce at least one of the two given views, so they are incorrect. \[ \boxed{\text{(i), option (A)}} \]
