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I integrated the volume of a parabola rotated about the y-axis with
R_1 the bottom (larger)radius of revolution, R_2 the top (smaller)
radius of revolution, and h = vertical distance between the bottom and top:
Parabola: x = a*y^2 + c
a = (R_2 - R_1)/h^2
c = R_1
V= pi*h*((3*R_2^2 + 4*R_1*R_2 + 8*R_1^2)/15)
V_cyl = pi*h*R^2
R = sqr((3*R_2^2 + 4*R_1*R_2 + 8*R_1^2)/15)