Question

A square pyramid sequentially passes through three cut-outs, namely, 1, 2, and 3, without changing its orientation. Each cut-out has a circle with notches as shown. The cut-outs scrape off parts of the pyramid as it passes through them. Which option shows the CORRECT Side View of the remaining part of the pyramid at the end of the sequence? 

• A. A
• B. B
• C. C
• D. D

Hint:

For 3D shapes passing through cut-outs, visualize how each cut affects the geometry of the object and consider the sequence of changes.

Answer 1

The Correct Option is C

Step 1: The pyramid enters cutout 1 first. Any part outside its circle and notch boundary gets sheared off.

Step 2: That reduced shape then enters cutout 2. Anything sticking out past its circle and notch outline gets removed too.

Step 3: Cutout 3 repeats the same shearing action on what remains. The shape that exits fits inside all three openings, not just the last one.

Step 4: Drawing that final shape from the side gives the silhouette in option C. It is the only option consistent with being trimmed by all three cutouts in sequence.

Answer 2

Look at what stays fixed while the pyramid gets scraped, instead of tracking each cut on its own.

1. Option A: Keeping one whole face edge fully intact breaks the rule that a notch removes a bite wherever a cutout's notch meets that face. This cannot be the final shape.
2. Option B: A silhouette missing one of the three expected notch marks means one scrape event is unaccounted for. Each of the three cutouts should leave its own mark somewhere on the shape.
3. Option C: The pyramid's apex and its general taper stay invariant, since scraping only removes surface material near the base and mid sections where the circles sit. This option preserves both the taper and all three notch marks correctly.
4. Option D: A notch mark on the upper part of the pyramid breaks the invariant that only bands touched by a cutout's circle get scraped. The upper region was never inside any of the three circles.

Track which parts of the pyramid must stay untouched and which bands each cutout can reach. Only option C fits every constraint at once.

the correct answer is Option C.