It depends on the formula that describes the surface itself. "Curved surface area" is not enough information to answer the question.
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3*pi*r2
Curved surface area of a cylinder excluding the two end pieces = 2*pi*radius*height in square units.
The curved surface area of a cone is: pi*radius*slant length.
Zero. A cube does not have a curved surface area.
It called the curved surface area. There is no special name for it.