Alright, pi*r*2 isn't even the formula for the area of a circle, but I think you meant to write it as pi*r^2.
Well, this is kind of confusing to me, but I don't think a math formula is a machine, or a device for looking at stars.
And although (D) is the only choice left, I don't think a model is the correct answer, since models are used to represent objects that are too large or too small for the human eye to comprehend. But still, it's the only choice that might make sense, so, (D) I guess.