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

[popeyespappy]

How about I just give everyone icing-less cake and I keep the icing all to myself?

I do make a pretty badass icing, if I do say so myself. Many of my fellow students in school begged me to make their graduation cakes for them.

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And therein lies the solution:

You scrape all of the icing off the cake first, then cut the cake into five equal portions. Then you take the icing and divide it into five equal portions and let everyone put their share of icing on their share of cake.


/thread.

I know what he was trying to say, but he is trying to make the problem harder than warranted for a middle school math question. The intent of the problem was to solve for volume (cake) and surface area (icing). It gets a lot more complicated if you want to solve for the volume of the cake and the volume of the icing. Let's say we have a 20x20x5 cake covered top and sides with 0.5 cm of icing.

Cake volume: 20x20x5=20003cm
Cake each: 2000/5=4003cm

Icing volume: (21x21x5.5)-(20x20x5)=425.53cm
Icing each: 425.5/5=105.13cm

That sounds easy enough. Just cut it up so that everyone gets 4003cm of cake and 105.13cm of icing. The problem is if you solve for icing volume the cake is off. If you solve for cake the icing is off because of the 4 corners. Each corner has 1.3753cm of icing and you can't divide those 4 corners 5 ways without separating them from everything else first.

ETA: In the solution I posted on page 3 a 20x20 cake with a 1/2 cm of icing on the top and sides everyone would have received 4003cm of cake, but 3 of the pieces would have had 85.3753cm of icing and the other two would have had 84.68753cm of icing. There is no simple solution for the volume plus volume problem of this sort when the number of pieces isn't a multiple of the corners.