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Volume of an Ellipsoid

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Calculate the volume and surface area of an ellipsoid using its three semi-axis lengths.
Semi-axis a
Semi-axis b
Semi-axis c
Volume V 
Surface Area S 
\(\normalsize Ellipsoid\\ (1)\ volume:\hspace{45px} V={\large\frac{4}{3}}\pi abc\\ (2)\ surface\ area:\\ \hspace{30px} S=2\pi\left(c^2+abxE(x,k)+{\large\frac{bc^2}{ax}}F(x,k)\right)\\ \hspace{30px} x=\sqrt{1-{\large\frac{c^2}{a^2}}}\ ,\hspace{10px}k={\large\frac{\sqrt{1-{\large\frac{c^2}{b^2}}}}{x}},\hspace{10px}a\ge b\ge c\\ F(x,k)\ 1st\ incomplete\ elliptic\ integral\\ E(x,k)\ 2{\small nd}\ incomplete\ elliptic\ integral\\\)

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