the statue of corcovado can be reached exclusively via the train at the base of it, or via the official minivans located at estrada da paineiras.

the entrance to the train is located across from rua cosme velho 470, in front of the igreja são judas tadeu, as seen on this google map.   

a taxi ride from the zona sul to the corcovado train is about br$ 25. alternatively  the buses 583 and 584  'cosme velho'  stop along the zona sul and take right at the train.