Check out "horizontal cylindric segment" in Wolfram Alpha Online. That is the correct term for the solid you are looking for.
Wolfram Alpha - "The solid cut from a horizontal cylinder of length L and radius R by a single plane oriented parallel to the cylinder's axis of symmetry (i.e., a portion of a horizontal cylindrical tank which is partially filled with fluid) is called a horizontal cylindrical segment."
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A cylinder? A cylinder is still a cylinder regardless of how long it is.
Another cylinder
The radius of a cylinder is half the thickness of its circular cross section.
It is half the thickness (diameter) of the circular cross-section of the cylinder.
A cylinder is a 3-dimensional object. A pyrimad is a typographic error!