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

1. A: Mentally rotating the base cross-shaped solid to different viewing angles reproduces this silhouette at one of those angles.
2. B: No rotation of the base solid reproduces this silhouette, since the arms bend into an L-shape here, which the base solid's straight arms cannot do.
3. C: Continuing to mentally rotate the base solid, another one of those angles reproduces this silhouette exactly.
4. D: No rotation of the base solid reproduces this silhouette, since the column-to-row proportions here do not match the base solid at any angle.

Trying the base solid at different viewing angles reproduces options A and C, but not B or D.

So the correct answer is A.

Answer 2

A third check is to measure each arm of the cross shape separately, in cubes, rather than judging the whole silhouette at once.

1. A: The vertical arm here has 3 cubes and the horizontal arm has 3 cubes, sharing the centre, matching the base solid's arm lengths exactly.
2. B: The arms here are bent partway along their length, so measuring a single straight arm length does not even apply the same way, marking this as a different solid.
3. C: Measured arm by arm, this option again gives 3 cubes and 3 cubes sharing the centre, matching the base solid.
4. D: Measuring arm by arm here gives a longer vertical arm and a shorter horizontal arm than the base solid, so the arm lengths do not match.

Only A and C have arm lengths that match the base solid exactly.

So the correct answer is A.