Question

how is carbon cycled through the hydrosphere and geosphere?

Answer 1

Hydrosphere is liquid sphere of earth and geosphere is the solid part of Earth.
in Hydrosphere, carbon exists in acid rain, when carbonic acid is present in aqueous solution or in acids in rocks that weather them.
In Geosphere, carbon exists as components of rocks and as hydrocarbons, like Nafta and Bitumen.