Question

The intersection of two cubes cannot be

• A. cube
• B. triangle
• C. rectangle
• D. none of these

Answer 1

The Correct Option is A

To determine the possible shapes formed by the intersection of two cubes, let's analyze how geometric intersections work. When two cubes intersect, the intersection is a subset of both volumes, which is a three-dimensional shape.

Now, consider the given options:

Shape	Possibility
Cube	Not possible
Triangle	Possible
Rectangle	Possible
None of these	N/A

Explanation:

1. Cube: For the intersection of two cubes to be another cube, every edge and face must perfectly align into another cube structure, a scenario which is not geometrically feasible unless the cubes are identical, which technically does count as an "intersection" in different contexts, but not in the conventional sense intended here.

2. Triangle: Possible when two cubes intersect along a plane that slices through corners or edges.

3. Rectangle: Possible if the intersection occurs along adjacent surfaces of both cubes.

4. None of these: This option serves as a catch-all for any other unexpected intersection shape.

Thus, the intersection of two cubes cannot form another cube. The correct answer is cube.