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Which of the following represents all points on or inside a circular cylinder of radius 4 having the x-axis as its axis?

1) A plane parallel to the x-axis
2) A plane parallel to the y-axis
3) A plane parallel to the z-axis
4) A plane perpendicular to the x-axis

User Pellay
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1 Answer

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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.

User Pmdj
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