The areal and volume must then be equal for all persons. As we don't know the cake's height, we have to give all people the same amount of frosting from the sides. Apart from that, the volume they gain should also be equal.
This means that, as long you cut vertically, all people should have 1/5 of the areal of frosting from the sides, and 1/5 of the areal of the frosting from the top. They will thus get the same amount of cake.
However, how do we find the areal of the frosting from the sides? Well, as we may write the areal of the sides as 4*s*h, where both s and h is unknown, we can, as long we cut vertically, skip the h because this will be fixed by the vertical slices. The amount of frostings on each side each person will get is then 4l/5, or 4/5*s where s is the width/length of the cake.
![[Image: cakers8.png]](http://img110.imageshack.us/img110/5877/cakers8.png)
So Alloy's right, this will then be at least one right possibility. 3 other ways is made by rotating this pattern 90 degrees.
Edit: Well, I just saw perpendicular, but I couldn't exactly figure out where "base" is. If you mean by cutting it vertically, then the upper is correct. If though, they mean that all cuts should be perpendicular, then the upper answer is wrong, though they get the same amount of cake and frosting.
Cut the cake into 25 equal squares (4 cuts on each side). Now, let's say that the cake's sides will equal 1 frosting unit on the sides, and the corners will equal 2 frosting units on the sides. We have 4 corners, and 3 * 4 sides, therefore we got 20 frosting units which we will have to divide to everyone.
There are numerous ways to get the right answer, this is only one of the ways:
![[Image: hmmsgv4.png]](http://img129.imageshack.us/img129/5356/hmmsgv4.png)
This means that, as long you cut vertically, all people should have 1/5 of the areal of frosting from the sides, and 1/5 of the areal of the frosting from the top. They will thus get the same amount of cake.
However, how do we find the areal of the frosting from the sides? Well, as we may write the areal of the sides as 4*s*h, where both s and h is unknown, we can, as long we cut vertically, skip the h because this will be fixed by the vertical slices. The amount of frostings on each side each person will get is then 4l/5, or 4/5*s where s is the width/length of the cake.
So Alloy's right, this will then be at least one right possibility. 3 other ways is made by rotating this pattern 90 degrees.
Edit: Well, I just saw perpendicular, but I couldn't exactly figure out where "base" is. If you mean by cutting it vertically, then the upper is correct. If though, they mean that all cuts should be perpendicular, then the upper answer is wrong, though they get the same amount of cake and frosting.
Cut the cake into 25 equal squares (4 cuts on each side). Now, let's say that the cake's sides will equal 1 frosting unit on the sides, and the corners will equal 2 frosting units on the sides. We have 4 corners, and 3 * 4 sides, therefore we got 20 frosting units which we will have to divide to everyone.
There are numerous ways to get the right answer, this is only one of the ways: