A cake has dimensions $15'' \times 15'' \times 3''$. It is
frosted on the sides and top. How can it be divided into 5 pieces so that each
piece has the same amount of cake and the same amount of frosting? What
if the dimensions are changed? What about 6 pieces? 7 pieces? $n$ pieces?
Tags: non-calculus, geometry, linear, word-problem, generalization, v--g--a, t2, c3
In case you were wondering, there is a nice solution which doesn’t involve non-vertical cuts, scraping all the frosting off, and other tricks. The solution even generalizes to more pieces.
– Dave Kung 1998-08-09
Great geometry problem with more than one solution. Also a good project for students to work on (whose math skills are from geometry and up). This problem was done by a couple of my students and the class seemed to enjoy their presentation very much. Especially the rectangular cake that was brought in and shared after the talk. Mmmmmmm….Chocolate!!
– Darrin Visarraga 1998-08-09