Can you cut a cake fairly to solve this middle school math problem?

[Whateverist]

Actually, as I think about it, my stepson was two or three years into high school math when he showed me this problem. It only became a middle school math problem when I started giving it out to advanced sections of 8th graders - greatly simplified. I always gave the problem straight to begin with but would then give them a written statement of the problem with a good deal of structure added. Here is a hint by way of the simplified structure I would provide.

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I would provide them with an orthographic projection along with actual dimensions of five inches on a side and a height of 2 inches. I'd also give them a view of the cake from above showing dotted grid lines every one inch. If you think of the frosting as painted on very thin, it also helps.

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