The Upright Cylinder.

Observing the angle of the light source as it illuminates half the cylinder is neccessary to understand its shading. As the birds-eye illustration below demonstrates, the part of the constantly curving exterior surface of the cylinder that receives the light most directly (squarely) happens to be nearest the source.  However, the interior of the cylinder is also illuminated, at least near the top, and, since it curves in a opposite manner, the part of it that is the high value is farthest from the light.  This change of angle produces a lowering of value on the illuminated surface toward the terminator.
The shading of the interior curvature of the cylinder is the reverse of the exterior.  The relative positions of the interior and exterior terminators are on a diameter of the cylinder's circular cross section.
The reflected light from the table washes out some of the terminator and shadow at the bottom.  Notice the darkening of the cast shadow near the cylinder's base and its sharp and fuzzy edge.

As illustrated, the terminator is that demarcation of the directly illuminated surface from the part of the surface that is in shadow.  It occurs on a cylindrical surface, or any curved surface, where the a line to the light source is tangent to the surface.
Typically the lowest value area on the shadow side on the exterior of any object occurs adjacent to the terminator.  Many beginners assume the darkest area is on the edge farthest from the light.  This is understandable but wrong.  The bounce back of reflected light is generally illuminates the back edge of objects, like this cylinder, sufficient to raise its value significantly.

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