Cylinder and Plane Intersection

Correct Answer

B — a circle

Concept and Reasoning

In cylindrical coordinates, ρ = 2 is a right circular cylinder of radius 2 about the z-axis, while z = 1 is a horizontal plane. Their intersection is x² + y² = 4 at z = 1, which is a circle.

Calculation / Key Relation

ρ=2 ⇒ x²+y²=4

z=1

Intersection: x²+y²=4 at z=1 ⇒ circle

Exam Takeaway

Cylinder ∩ horizontal plane = circle.

Common Mistake

Do not interpret ρ=2 as a sphere; spherical radial distance is normally denoted r.