First, the legs of the trapezoid are given linear equations. Using the the coordinates, we obtain y = 4/3*x - 4/3 for one and y = -4/3*x + 16 for the other. In terms of x, they are x = 3y/4 + 1 and x = -3y/4 + 12. The volume of the trapezoid's revolution about the x-axis can be obtained by integrating pi*r^2 for the two lines and the horizontal line y = 4, where r is the equation in terms of x. Adding up the integrals yields to 112pi. For the revolution about the y-axis, the washer formula is used, which is pi*R^2 - pi*r^2 where R is the equation of the right leg in terms of y and r is the equation of the left leg in terms of y. Integraion leads to 416pi. The ratio of the two volumes is about 3.7.