The word "base" is just fine for this purpose.
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The base of a cylinder is called a circular base. It is a flat, circular surface that forms the top and bottom of the cylinder.
the base of a cylinder is a circle.
The base of a cylinder is the circular part. What exactly are you trying to DO with it?
To find the base area of any prism, including the circular prism called cylinder, divide the volume by the height.
Area of the base of a cylinder = pi*radius2
A circular base if facing downward. A circular face if facing to the sides.