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?
Show Hint
Match the front view outline first to eliminate options, then confirm with the top view.
Step 1: Understand what front view and top view mean.
The front view is what you see when you look at the structure straight on from the front, and it shows the height and width flattened onto a vertical plane. The top view is what you see when you look straight down at the structure, and it shows the length and width flattened onto a horizontal plane.
Step 2: Note the shape given in Panel I.
Panel I gives a stepped front view, where the outline rises in a staircase pattern, and a top view with a matching notch, since the same physical structure must produce both projections at once. Any candidate structure in Panel II must reproduce both of these outlines exactly, with no missing cube and no extra cube.
Step 3: Check structure (i).
When structure (i) is viewed from the front and from the top, the block at the corner does not sit where Panel I needs it. Its top view does not carry the same notch as Panel I, so it fails to match and is ruled out.
Step 4: Check structure (ii).
Structure (ii) has an extra cube on one side that is not present in Panel I's outline, and its front view comes out wider than the stepped shape shown in Panel I. So structure (ii) is also ruled out.
Step 5: Check structure (iii).
Structure (iii) is close to the required shape but has one cube placed one row further back than Panel I demands. This shifts its front view outline out of step with Panel I, even though the top view looks similar at a glance. So structure (iii) does not match either.
Step 6: Check structure (iv).
Structure (iv) reproduces the exact stepped outline seen in the front view of Panel I, with the cubes rising in the same staircase order, and its top view carries the same notch in the same position. Both projections line up with Panel I with nothing extra and nothing missing.
Final Answer:
Only structure (iv) gives both the front view and the top view shown in Panel I.
\[ \boxed{\text{(iv)}} \]
