Question

A cylinder is cut by a curved surface as indicated by the dotted line in the figure. The top portion of the cylinder is removed. Which option shows the resultant view when seen from the direction indicated by the arrow? 

• A. A
• B. B
• C. C
• D. D

Hint:

For 3D visualization problems, break the object down into its key features (top, bottom, sides). Determine how each feature will look from the specified viewpoint and then combine them to form the final 2D shape. Eliminate options that get any single feature wrong.

Answer 1

The Correct Option is D

Step 1: Understanding the Concept:
The problem requires us to visualize a 3D object after a cut has been made and then determine its 2D appearance (silhouette) from a specific viewpoint.
Step 2: Key Formula or Approach:
We need to mentally construct the shape and then project it onto a 2D plane as seen from the arrow's direction. We should consider the outlines of the object: the base, the sides, and the new top surface created by the cut.
Step 3: Detailed Explanation:
1. The Base: The cylinder is standing upright. When viewed from the side (as the arrow indicates), the circular bottom edge will appear as a straight, horizontal line. This immediately eliminates option A, which has a curved bottom.
2. The Cut Surface: The dotted line in the diagram represents the profile of the new top surface. It is a curve that is higher on one end and lower on the other. When we view the object from the side, the top outline of our 2D shape will be exactly this curve.
3. The Overall Shape: Combining these observations, the resulting 2D view must have a flat horizontal bottom and a top outline that matches the curved dotted line.
4. Evaluating the Options: - A: Incorrect, the bottom is curved. - B: Incorrect, this is a triangle, meaning the top cut would have to be a cone, not a curve. - C: Incorrect, this oval shape represents what the cut surface would look like if viewed from directly above, not the side profile of the remaining object. - D: This shape correctly shows a straight horizontal base and a curved top profile that matches the dotted line in the question. This is the correct side view silhouette. Step 4: Final Answer:
Option D accurately represents the resultant view from the direction indicated by the arrow.