There is a square cake at a birthday party attended by a dozen people. How can the cake be cut into twelve pieces, so that every person gets the same amount of cake, and also the same amount of frosting?
Remark: The decoration of the cake is put aside, nobody eats it.
Divide the boundary of the cake into twelve equal parts, then simply make cuts passing through the separation points and the center. This way all tops and bottoms of the formed pieces will have equal areas, and also all their sides will have equal areas. Since all pieces have the same height, their volumes will be equal as well.