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

[popeyespappy]

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5 cuts. Each running from the center to the outside edge. In the case of a 20 x 20 x 5 cake each cut needs to be 16 linear centimeters along the outside edge. That would give everyone 160 square centimeters of icing and 400 cubic centimeters of cake.

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Mathematically this is a easy and clear solution, but I rejected it because I missed the part about the cake being a square, and thought the original question indicated the dimension, and presumably the aspect ratio, of the cake didn't matter.  This implies the solution had to be elegant enough to not require careful measurements of the aspect ratio of the cake to come up with angles of the cuts.

Correct. This simple solution only works for a square (or round) cake like the one Whateverist listed as an example. I'm not even sure there is a solution that yields equal shares of surface area (icing) and volume (cake) for an oblong shape because if you solve for surface area the volume is unequal. If you solve for volume the surface area is unequal.