Calculator and formulas for calculating an elliptic cone
This function calculates various properties of an elliptic cone. To perform the calculation, enter the two radii and the height of the elliptic cone. Then click on the 'Calculate' button.
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Base area
\(\displaystyle A = a·b·π \)
Lateral area
\(\displaystyle M =\frac{1}{2} \int_0^{2·π}\sqrt{a^2·b^2+h^2· (a^2·sin^2(t)+b^2·cos^2(t))} \;\;dt\)
With the simplified formula you get an estimate.
\(\displaystyle M >\frac{π}{2} · \left(a·\sqrt{b^2+h^2}+b·\sqrt{a^2+h^2}\right) \)
Surface
\(\displaystyle S = A+M \)
Volume
\(\displaystyle V= \frac{h · a·b·π }{3} \;\;= \frac{h ·A }{3} \)
*) The lateral surface is calculated using an integral, but is estimated here using the simplified formula. The estimate is slightly below the exact value. With a=2, b=3 and h=4, the estimate returns the value 36.78... The exact value is 36.9...
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