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Typically, a face is defined as a polygon that is a flat surface of a solid figure. That means that if we can consider a circle to be a polygon, then a cylinder actually has two faces, namely the circles that form the two bases. So, the question becomes: Can we consider a circle to be a polygon?
A polygon is a closed plane figure bounded by three or more line segments. Three or more means that then number of sides can be as large as you like. A circle is actually the limiting figure for an n-sided polygon as n increases without bound. In other words, it is perfectly proper to say that a circle is an infinite-sided polygon.
So, we have established that faces must be flat and faces must be polygons and that a circle is, in fact, a polygon. Therefore a right circular cylinder has two faces. In fact, we can generalize even further to include oblique cylinders and cylinders where the base is elliptical rather than circular.
Given all of that, does a sphere have a face? No. And while we are at it, a cone has one face.