Slicing Shapes

1. What is the maximum number of pieces into which a pancake can be cut by n straight cuts, each of which crosses each of the others?
2. What is the maximum number of pieces that can be produced by n simultaneous straight cuts of a flat figure shaped like a crescent moon?
3. Into how many parts can the plane be divided by intersecting circles of the same size? Of different sizes? By intersecting ellipses of different sizes?
4. How many pieces of cheesecake can be produced by n simultaneous plane cuts of a cylindrical cake?
5. Into how many regions can space be divided by intersecting spheres?
6. What is the maximum number of pieces that can be produced by n simultaneous plane cuts through a doughnut?