Introduction:
A cube is a three-dimensional geometric shape with six equal square faces. It is a special type of rectangular prism where all the edges have the same length. In this question, we are given four options and we have to determine which option correctly describes how a cube can be obtained.

Explanation:
To understand how a cube can be obtained, let's evaluate each of the given options:

Option A: Extruding a square
Extrusion is a process where a two-dimensional shape is extended into the third dimension. In this case, if we extrude a square along its normal vector (perpendicular to the square's plane) by the same length as its side, we will obtain a cube. Each face of the cube will be congruent to the original square.

Option B: Extruding a rectangle
Extruding a rectangle will result in a rectangular prism, not a cube. The rectangular prism will have six rectangular faces, and only if all the faces are congruent squares will it be a cube.

Option C: Rotating a square about center
Rotating a square about its center will not result in a cube. It will create a three-dimensional shape called a square pyramid, where the base is a square and the other four faces are triangles.

Option D: None of these
This option is incorrect because option A, extruding a square, is the correct method to obtain a cube.

Conclusion:
In summary, a cube can be obtained by extruding a square along its normal vector. The resulting shape will have six congruent square faces. Extruding a rectangle or rotating a square about its center will not result in a cube. Hence, the correct answer is option A.

Option a