# Volume of an elliptic truncated cone Calculator

## Calculates the volume, lateral area and surface area of an elliptic truncated cone given the lower and upper semi-axes and height.

 lower semi-axis a1 lower semi-axis b1 upper semi-axis a2 height h 6digit10digit14digit18digit22digit26digit30digit34digit38digit42digit46digit50digit 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$\normal Truncated\ elliptic\ cone\\(0)\qquad upper\ semi-axis:\hspace{15} b_{2} = \frac{b_{1}a_{2}}{a_{1}} \\(1)\qquad volume:\hspace{53} V= \frac{\pi b_{1}h }{3 a_{1} } ( a_{1}^{2} + a_{1}a_{2} + a_{2}^{2} ) \\(2)\qquad lateral\ area: \\\ \hspace{15} F= \left ( 2 a_{1} \sqrt{b_{1}^2+ \left( \frac{h a_{1}}{a_{1}-a_{2}} \right)^{2}} -2 a_{2} \sqrt{ \frac{b_{1}^2 a_{2}^{2}}{a_{1}^{2}} + \left( \frac{h a_{2}}{a_{1}-a_{2}} \right)^{2}} \right ) E \left( \sqrt{ \frac{1- \frac{b_{1}^{2}}{a_{1}^{2}} }{ 1 + \frac{b_{1}^{2} (a_{1}-a_{2})^{2}}{h^2 a_{1}^{2} } } } \right) \\\ \hspace{400} ( a_{1} \gt b_{1} ) \\\ \vspace{5} \\\ \hspace{30} = \left ( 2 b_{1} \sqrt{a_{1}^2+ \left( \frac{h a_{1}}{a_{1}-a_{2}} \right)^{2}} - \frac{ 2 b_{1} a_{2} }{a_{1}} \sqrt{ a_{2}^{2} + \left( \frac{h a_{2}}{a_{1}-a_{2}} \right)^{2}} \right ) E \left( \sqrt{ \frac{1- \frac{a_{1}^{2}}{b_{1}^{2}} }{ 1 + \frac{(a_{1}-a_{2})^{2}}{h^2} } } \right) \\\ \hspace{400} ( a_{1} \lt b_{1} ) \\\ \vspace{5} \\\ E(k)\ :\ 2{\small nd}\ complete\ elliptic\ integral\\ \\\vspace{5}\\\vspace{5}(3)\qquad surface\ area:\hspace{10} S=F+\pi a_{1} b_{1} + \pi a_{2} b_{2} \\$
Volume of an elliptic truncated cone
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