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MathCalculus

Cylindrical Coordinate System: Convert a Shifted Cylinder Equation

Convert a shifted cylinder equation to cylindrical coordinates while preserving the r = 0 coordinate cases.

Question

Rewrite the surface equation x2+y2−16x=0x^2+y^2-16x=0 using cylindrical coordinates (r,θ,z)(r,\theta,z).

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Evidence boundary

The surface equation and conversion request come from OpenStax Calculus Volume 3, Section 2.7, Exercise 383. This independent solution retains the r=0 coordinate cases. The cylinder identification is a check, not an extra original subquestion.