> How does carbon dating work on a statue?

It doesn't, and the stone itself is typically hundreds of millions or even billions of years old.

However, many ancient artifacts are found buried in the ground, and it is often possible to carbon-date organic material in the soil surrounding the artifact, which produces an estimate for when it was buried. This is typically combined with historians' estimates for when the culture that presumably produced the artifact flourished, though uncertainties of several millennia remain in some cases.