Question Details

A block with a trapezoidal cross-section is placed over a block with rectangular cross section as shown above. Which one of the following is the correct drawing of the view of the 3D object as viewed in the direction indicated by an arrow in the above figure?

Options

A

B

C

D

Correct Answer :

Solution :

The correct answer/option is:
Option 1: [IMAGE] (corresponding to the first image in the options list).

Step-by-Step Explanation:

1. Analyze the 3D Object:
The given 3D object consists of two blocks:
• A lower block with a rectangular cross-section.
• An upper block with a trapezoidal cross-section placed on top of the lower block.
By inspecting the 3D view in the question image, we can observe that the back face of the upper block is aligned flush (coplanar) with the back face of the lower block, forming a single continuous vertical plane. The front face of the upper block is slanted (inclined) downwards and meets the top surface of the lower block, leaving a flat, exposed portion of the lower block's top surface at the front.

2. Determine the Viewing Direction:
The arrow indicates that the observer is looking at the 3D object from the right side along its length.
When viewing from this direction:
• The back of the object (the vertical, flush face) will appear on the right side of the 2D projection.
• The front of the object (where the upper block is slanted and the lower block extends forward) will appear on the left side of the 2D projection.

3. Construct the 2D View:
Lower portion: The end face of the rectangular lower block is viewed directly, which appears as a simple rectangle.
Upper portion: The trapezoidal cross-section of the upper block is visible sitting on top of the rectangle.
Alignment:
    - On the right side, the vertical back edge of the top block and the vertical back edge of the bottom block line up to form a continuous straight vertical line.
    - On the left side, the top block's slanted edge slopes downward from the flat top surface and ends on the horizontal boundary separating the two blocks, leaving the left part of the lower block's top edge visible.

4. Compare with the Options:
Option 1 (Correct): Correctly shows the bottom block as a rectangle, with the upper block having a vertical right edge aligned flush with the bottom block, and a slanted left edge ending on the top surface of the bottom block.
Option 2 (Incorrect): Shows the slanted line extending all the way through the bottom block, which is incorrect because the bottom block has a solid rectangular cross-section.
Option 3 (Incorrect): Shows the slanted edge on the right and the vertical edge on the left, which is a mirrored view (viewed from the opposite direction).
Option 4 (Incorrect): Shows a completely different projection that does not match the side profile.

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