We don't cut cakes this way!
Suppose you are cutting a cylindrical cake. Assuming that you cannot move the pieces, what is the maximum number of pieces you can get by cutting the cake 3 times?
Clarification: The cuts are made straight and not curved.
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Each time we slice the cake, we can cut one piece into at most 2 pieces. So after the first slice, we have at most 2 pieces. After the second slice, we have at most 4 pieces. After the third slice, we have at most 8 pieces.
Let us now show that 8 is indeed possible. Because the cake is 3 dimensional, we can cut it into half in the x, y and z directions. This gives us 8 slices of cake, similar to how there are 8 "quadrants" in 3-dimensions. See the image:
Thus, maximum number of slices is 8.