What is the equation for a 3D cylinder in Murray Spiegel's Advanced Calculus?

[coverband]

1. In Murray Spiegel's Advanced Calculus, in solved problem 10.18 he describes a cylinder as having equation x^2 + y^2 = ax. Surely this equation is for a 2-D object. Whats going on as a cylinder is 3D?

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The Attempt at a Solution

 

[Mark44]

1. In Murray Spiegel's Advanced Calculus, in solved problem 10.18 he describes a cylinder as having equation x^2 + y^2 = ax. Surely this equation is for a 2-D object. Whats going on as a cylinder is 3D?

No, it's a 3D object, with z being arbitrary. If you look at the trace of this cylinder in the x-y plane (i.e., z = 0), you get a circle. For any z = k, some constant, you also get a circle, but this time in the plane z = k.