Final answer:
Rotating a square about a line passing through its center produces a cylinder.
Step-by-step explanation:
When a square is rotated about a line passing through its center, the resulting solid 3D object is called a cylinder. A cylinder has two circular faces called bases, which are parallel and congruent, and a curved surface connecting the bases. The distance between the bases is equal to the side length of the square.
For example, consider a square with side length 4 units. When this square is rotated 360 degrees about a line passing through its center, a cylinder with height 4 units and radius 4 units is formed.
It's important to note that the line of rotation for a solid object is typically represented as a straight line, not a squiggly line as described in the question.