How were the giant Buddha statues of the 7th century created, and why?

by Finely_drawn

The late Bamiyan Buddhas of Afghanistan, and the Leshan Giant Buddha in the Sichuan Province, are monolithic statues carved into sheer rock face. How would this have been achieved? What was the religious significance behind the placement of them?

not_stoned

I have a related question - I've read that statues of the Buddha were first created by Indo-Greek culture, is this true? If so, was it this style that then spread all the way to East Asia? Do the Bamiyan Buddha's have any influence from this Indo-Greek style?