Question

A cylinder \(P\) is cut by a cylinder \(Q\) as shown. Choose the option which shows the shape obtained after unrolling cylinder \(P\).

• A. A
• B. B
• C. C
• D. D

Hint:

When analyzing intersecting 3D shapes, consider how the geometry of the cut transforms when projected onto a flat surface.

Answer 1

The Correct Option is B

1. Analysis of the Cutting Process:
- Cylinder \(P\) is intersected by cylinder \(Q\), creating a cut along the surface of \(P\).
- When cylinder \(P\) is unrolled into a flat sheet, the intersection with cylinder \(Q\) forms a pattern based on the geometry of the cut.
2. Shape of the Cut:
- The intersection of two cylinders forms a curved shape.
- The unrolled surface of \(P\) will display a sinusoidal-like wave pattern due to the curved nature of the intersection, as seen in \(B\).
3. Options Analysis:
- Option A: Shows an incorrect pattern that does not match the geometry of the intersection.
- Option B: Accurately represents the sinusoidal-like pattern formed by the intersection, matching the unrolled view of cylinder \(P\).
- Option C: Represents an unrealistic pattern for the given configuration.
- Option D: Does not align with the geometric nature of the intersection.
Conclusion: The correct shape obtained after unrolling cylinder \(P\) is shown in \(B\).