You can see this cake is in the shape of a cylinder.
What is the maximum number of slices one can divide it into with straight cuts?
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Note that if we were viewing the cake as 2-dimensional, the answer would be 7 , with each cut intersecting with the other two at two distinct points (one each).
However, since the cake is 3D, we can cut the cake into two smaller cakes and then layer them to make four more slices in each small cakes, resulting in
8
slices. (Note that this can be visualized as cutting once along each dimension: the length, the width, and the height.)
To prove 9 and 10 are impossible: Note that the first slice must divide the cake into two parts. The second slice either intersects with the first slice, causing 4 slices, or doesn't, causing 3 slices. Note that the next slice can either cut each slice in half or not, thus the maximum we can have is 8. We have proven this is achievable above.