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**1. Homework Statement**

Describe in words the region of R3 represented by the inequality x^2 + z^2 <= 9

**2. Homework Equations**

Equation of a sphere= (x-h)^2 + (y-k)^2 + (z-l)^2 = r^2

**3. The Attempt at a Solution**

Since there is no y value in the given inequality, I stated that it would be points in or on a circle on the xz-plane with center at the origin, and the radius is 3 with respect to the xy-plane.

However, my book says this inequality describes a cylinder of radius 3 with y-axis. Can someone explain this to me please? How can it be a cylinder? And why is the radius with the y-axis and not with the xy-plane?

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