Question

Two views of a solid are shown. Which of the options is/are the view/s of the same solid? 

• A. A
• B. B
• C. C
• D. D

Hint:

When analyzing 3D objects from 2D views, focus on the core structure and connectivity of the components (in this case, cubes). Count the number of units in each arm or section and check for consistency across all views.

Answer 1

The Correct Option is A

Step 1: Understanding the Concept:
This problem requires us to mentally construct a 3D object from two different isometric views and then identify which of the options represent other possible views of that same object.
Step 2: Detailed Explanation:
First, let's analyze the solid shown in the two initial views. The object is a three-dimensional cross shape. It can be described as a central cube with arms extending from four of its faces. More specifically, it consists of a vertical column of three cubes and a horizontal row of three cubes, sharing the central cube. Let's call this the 'base object'. Now let's examine each option:

Option A: This view shows the base object from a slightly different angle, but the fundamental structure of a central cube with four arms is clearly visible and consistent with the initial views. The relative lengths and positions of the arms match. Thus, A is a valid view.
Option B: This object is fundamentally different. The 'arms' are not straight; they are bent into L-shapes. This does not match the structure of the base object. Thus, B is not a valid view.
Option C: This view shows the base object after it has been rotated. It's another valid isometric perspective of the same 3D cross structure. The arrangement of the cubes is consistent with the base object. Thus, C is a valid view.
Option D: This object has the proportions inverted. It appears to have a longer vertical column and shorter horizontal arms compared to the base object. It does not represent the same solid. Thus, D is not a valid view.

Step 3: Final Answer:
Options A and C are the only views that represent the same solid shown in the initial images.

Answer 2

The base solid is a cross shape built from a central cube with a vertical column of three cubes and a horizontal row of three cubes, sharing that central cube, so 5 unit cubes in total. Any true view of the same solid must show this same total unit count of 5 cubes, just seen from a different angle, so we can check each option by counting cubes instead of comparing silhouettes by eye.

1. A: Counting the cubes visible here, from this angle, still totals 5 cubes arranged as a central cube with four arms. This matches the base solid.
2. B: The arms here are bent into L-shapes rather than straight, which changes how the cubes connect to each other, so this is a different solid even if a cube count happened to be similar.
3. C: Counting the cubes from this angle again totals 5, arranged as the same central-cube-with-four-arms pattern, just viewed from another side.
4. D: The proportions here are inverted, with a longer column and shorter row, which changes the arrangement of cubes relative to the centre, so this does not match the base solid.

A and C both keep the same 5-cube cross arrangement as the base solid, just viewed from different angles.

So the correct answer is A.