Time for tea: cake division by lines

This 'cake division by lines' problem was used as an example in one of the lectures I attended at business school.

I've searched and it doesn't seem to be on the site yet, so here it is:

You have a cake and a knife.

You may cut the cake, with the knife, three times, in any direction.

You may not break the cake into pieces with your fingers (it's unhygienic) or in any other way apart from using the knife.

Each cut must be in a straight line.

What is the maximum number of pieces into which you can cut the cake?

The pieces don't all have to be the same size.

• puzzling.stackexchange.com/questions/2827/… – d'alar'cop Nov 10 '14 at 15:36
• @d'alar'cop: not the same puzzle, although they do both involve cake. 8 is not the correct answer to this one. – A E Nov 10 '14 at 15:38
• puzzling.stackexchange.com/questions/3801/… – d'alar'cop Nov 10 '14 at 15:41
• This is a vague question. What shape is the cake? If we don't know, we can't answer. It would be one thing if the answer relied on the idea that it doesn't matter what the shape was, but it does matter. – TheRubberDuck Nov 10 '14 at 21:03
• @EnvisionAndDevelop: Yes. The question tests whether you will make the assumption that the cake is a standard 'cake shape' such as round or rectangular. That's the puzzle. – A E Nov 10 '14 at 22:27