How is the effective piston area of a cone calculated?

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Yes, it is:
Sd = pi * radius ^2

or, since radius = Dia/2

Sd = pi*(Dia/2)^2 = (pi*(Dia)^2)/4

As Rodd says, you should include half of the surround. The easiest way to measure diameter is to measure across the diameter on opposite sides of the surround. See picture.
 

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