a = 
        1;

    b = 8;

    c = 10;

  

  

    ec = (c/a)^2  - 1;

    eb = (b/a)^2  - 1;
  

    mu = ArcTan[Sqrt[ec]];

  
  

    q  =  (eb*(1 + ec))/(ec*(1 + 
                  eb));
  

    p  =  (ec - eb)/ec;
  

    Fp  =  EllipticF[mu, p];

    Fq  =  EllipticF[mu, q];

    Ep  =  EllipticE[mu, p];

    Eq  =  EllipticE[mu, q];


    r2  =  Sqrt[(1 + eb)/(1 + ec)];

    r3  =  (Fp/ec) + Ep;
  

    Radius  =  (a/2)*(r2  +  
              Sqrt[ec]*r3);


    s2  =  Sqrt[ec*(1 + eb)];

    s3  =  (Fq/ec) + Eq;
  

    Surface =  
        2*Pi*(a^2) *(1 + (s2*
                  s3));


    Volume  =  (4  Pi/3)*a*b*c;
  

    alpha  =  (Radius*Surface)/(3*
              Volume);
  

    secondVirial = (Radius*Surface  +  Volume)/
          Volume;
  

    thirdVirial  =  (1 + 6*alpha + 
            3*alpha^2);

  

    N[Radius]

    N[Surface]

    Volume

    N[alpha]

    N[secondVirial]

    N[thirdVirial]