[TimT]

Its been 25 years or so since I last took any sort of advanced mathematics. Did the whole calculus based engineering program .....

I would say NO, since π (Pi) is irrational...

Occams Razor!

You will have to decide what value of π (Pi) is going to be used.... You could be scratching something out on a scrap of paper and use 3.14 or.. who knows how many places a computer take Pi too??

Interesting question

Also you would think the area is finite...

Say you had to measure the diameter of the circle, then use Pi in the calculation...... You would be using two irrational numbers then, since you can ever really measure to zero tolerance.... (picking nits)