Geometry problem

[Dr. S. Shapiro]

Dear Colleagues;

     Given

     Volume V of sphere = (4/3)*pi*r^3

     Volume V of spheroid = (4/3)*pi*a*b^2

          where axes 2a > 2b

     Eccentricity e of spheroid = [1 - (b^2/a^2)]^(1/2)

     then given a numerical value for the volume of a sphere, is there a 
unique value for the eccentricity of a spheroid with the same volume?

     For example, I have two spheres, one with a volume of 357 cm^3 and
the other with a volume of 372 cm^3.  What would be the eccentricities
of spheroids with volumes of 357 cm^3 and 372 cm^3?

     Kindly direct responses to me directly at 

                             toukie at zui.unizh.ch

Thanks in advance to all responders,
 
S. Shapiro
toukie at zui.unizh.ch