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Volume of an Elliptic Cone

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Calculate the volume, lateral surface area, and total surface area of an elliptic cone using its semi-axes and height.
Semi-axis a
Semi-axis b
Height h
Volume V 
Lateral Area F 
Surface Area S 
Reference)
Weisstein, Eric W. "Elliptic Cone." From MathWorld--A Wolfram Web Resource.
http://mathworld.wolfram.com/EllipticCone.html

\(\normalsize Elliptic\ cone\\ (1) volume:\hspace{53px} V={\large\frac{1}{3}}\pi a b h\\ (2) lateral\ area:\hspace{15px} \\\ F= 2 a \sqrt{b^2+h^2} E \left(\sqrt{ \frac{1- \frac{b^2}{a^2}}{ 1 + \frac{b^2}{h^2} } } \right) \\\ \hspace{200px} ( a \gt b ) \\\ \hspace{15px} = 2 b \sqrt{a^2+h^2} E \left(\sqrt{ \frac{1- \frac{a^2}{b^2}}{ 1 + \frac{a^2}{h^2} } } \right) \\\ \hspace{200px} ( a \lt b ) \\\ \\ E(k)\ :\ 2{\small nd}\ complete\ elliptic\ integral\\ \\ \\ (3) surface\ area:\hspace{10px} S=F+\pi a b\\\)

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