Problem 6.2.9
Here are the pictures we tried to draw on the board.

First, the two-dimensional region. The red rectangle will be the base of the equilateral triangle cross-section perpendicular to the x-axis. The intersection of the curves is the point (1,1). It is trivial to soleve by hand but you may find it useful to use Mathematica occasionally to check your solutions:

(We are only interested in the first solution above.)

Here is a 3-D view of the triangular cross-section.

Here's a bunch of 'em.