Calculator and formulas for calculating a truncated elliptic cone
This function calculates various properties of a truncated elliptic cone. To perform the calculation, enter the two radii and the height of the cone and the truncated cone. Then click on the 'Calculate' button.
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Cut off height\(\displaystyle j = h-i\)
Long semi-axis top\(\displaystyle c = \frac{a·j}{h}\)
Short semi-axis top\(\displaystyle d = \frac{b·j}{h}\)
Base area
\(\displaystyle A = a·b·π \)
Lateral area
\(\displaystyle M ≈ \frac{π}{2}·\left[\left(a · \sqrt{b^2 + h^2}+b·\sqrt{a^2+h^2}\right)-\left(c·\sqrt{d^2+j^2}+d·\sqrt{c^2+j^2}\right)\right]\)
With this simplified formula you get an estimate
Surface area
\(\displaystyle S = A+M \)
Volume
\(\displaystyle V= \frac{π}{3} · (h · a · b - j · c · d ) \)
*) The lateral surface is calculated using an integral, but is estimated here using the simplified formula. The estimate is slightly below the exact value.
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