Final answer:
The representation of all points on or inside a circular cylinder of radius 4 with the x-axis as its axis is a plane parallel to the z-axis.
Step-by-step explanation:
The student's question pertains to identifying the representation of all points on or inside a circular cylinder with radius 4, having the x-axis as its axis. Of the given options, the correct one is (3) A plane parallel to the z-axis. This is because any plane parallel to the z-axis will cut the cylinder across its radius at different points along the x-axis, covering all points on or inside the cylinder. Neither a plane parallel to the x-axis nor a plane perpendicular to the x-axis would accomplish this, as they would be tangential or cross-sectional, respectively. Planes parallel to the y-axis would show up as lines when intersecting the cylinder and do not represent all points on or inside it.