Apartments on hills versus flat areas

Thinking about Edward Tufte's information design and looking at the hills of Jerusalem from Yad Vashem... seeing the croppings of towns and neighborhoods in the area... a mathematical/geographical/architectural exercise:
Do cities get more living space for people's homes by building on hills rather than a flat open space? A hill offers more land surface area (physical x-y space) by going vertical (like a triangle, into the z-axis) than a flat area, but that doesn't necessarily translate into more living space. I'm considering apartments in this exercise, and they can be built as high as possible on a flat area, but can also be built as high on a hill, which has the advantage of allowing more residents to have a view outside their home (consider stacked apartments on a terraced landscape). I think a hill offers more space on which to build apartments, but I'm not sure if that always means more people can live in apartments there rather than a flat land area. More research needs to be done...