Figure P shows the top view of a circular table top with few objects arranged on it for a sketching class. Numbers 1 to 24 in figure P represent different directions around the table from which students are sketching the objects. Which option gives the directions from which the sketches in Figure Q and R are drawn?
Show Hint
In perspective problems, identify the object closest to the viewer in the sketch (the one that appears largest or lowest in the frame). Then, locate that object in the top-down view and determine the direction from which it would appear in the foreground.
Step 1: Understanding the Concept:
This problem requires spatial reasoning and the ability to correlate a 2D top-down view with 3D perspective sketches. We need to analyze the relative positions of the objects in the sketches (Q and R) and find the corresponding viewpoint numbers on the circular table (P).
Step 2: Detailed Explanation:
Let's analyze the arrangement of objects on the table from the top view (P). There is a central pyramid, surrounded by cylinders, cones, and cubes.
Analyzing Sketch Q:
Foreground: The sketch shows a tall cylinder in the immediate foreground, slightly to the left.
Middle ground: To the right of the cylinder is a cone, and behind both is the central pyramid. Another shorter cylinder is visible to the far right.
Arrangement: The viewer sees the tall cylinder, then the cone, then the pyramid in a line going away from them towards the right.
Matching to P: Looking at the top view P, this arrangement corresponds to viewing from position 1. From this viewpoint, the tall cylinder at the top is closest, the cone is just behind and to its right, and the pyramid is in the center. The other visible objects match this perspective.
Analyzing Sketch R:
Foreground: The sketch shows a cube in the immediate foreground.
Middle ground: Behind the cube, there are two cones, and behind them is the central pyramid. To the left and right are cylinders.
Arrangement: The cube is directly in front of the viewer. The two cones are positioned behind it, flanking the central pyramid.
Matching to P: This view corresponds to looking from the bottom of the diagram. Specifically, from position 16, a student would see the cube at the bottom edge of the table as the closest object. The two cones and the pyramid would be visible behind it, arranged as shown in the sketch.
Step 3: Final Answer:
The sketch in Figure Q is drawn from direction 1, and the sketch in Figure R is drawn from direction 16. This corresponds to option (C).
