Assigning Movie Textures to Individual Faces of the Inside of a Half-Sphere

As the title suggests I am attempting to apply movie textures to just one face of a half-sphere’s inside. How should I go about UV mapping each individual face (and applying specific textures to them) and how can I make it as painless as possible? The videos are rectangle and I want them to be projected right on to the face fully-scaled.

How can I do this, and is there a way to automate this?