I have a square cake. The cake is iced on top and all the sides. I need to cut the cake in 6 pieces all pieces getting the same amount of cake and icing. Please help me if possible with a diagram.
It is an interesting problem.
Bear in mind that any piece of cake with a vertex at the centre has an area proportional to the base (perimeter of the square).
You only have to divide the perimeter of the square into 6 equal lengths (wrapped around a corner if necessary).
See diagram for a possible solution at:
http://imageshack.us/photo/my-images/11/1314893656.jpg/
To cut a square cake into 6 equal pieces, you can follow these steps:
Step 1: Draw a diagram of the square cake. Label the corners as A, B, C, and D, starting from the top-left corner and moving clockwise.
A --------- B
| |
| |
| |
C --------- D
Step 2: Starting from corner A, cut a straight line to the opposite corner D, dividing the cake into two equal triangles.
A --------- B
| \ |
| \ |
| \ |
C --------- D
Step 3: From the midpoint of the line AD, cut a straight line to the midpoint of the side BC, creating another two congruent triangles.
A --------- B
| \ | |
| \ | |
|-----X |
C --------- D
Step 4: Finally, cut along the line AD from point X to point C, dividing the cake into two equal trapezoids.
A --------- B
/ \ | |
/ \ | |
X-----X | |
C --------- D
Now, you have successfully divided the cake into 6 equal pieces, each piece containing both cake and icing.