Rounded Cone Calculator
Calculator and formulas for calculating a rounded cone
This function calculates various properties of a rounded cone. To perform the calculation, enter the radii of the base and the spherical cap and the height of the truncated cone. Then click on the 'Calculate' button.
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Formulas for rounded cones
Cone base angle (\(\small{α}\))
\(\displaystyle α = arccos\left( \frac{R - r}{\sqrt{ h^2 + ( R - r )^2}} \right) \)
Height of cap (\(\small{i}\))
\(\displaystyle i = \sqrt{\frac{ r^2 }{\frac{ 2 }{ 1 - cos(α) } - 1 }} \)
Surface area (\(\small{S}\))
\(\displaystyle S = (R + r) · π · \sqrt{(R - r)^2 + j^2} + π· R^2 + π · (r^2 + i^2) \)
Volume (\(\small{V}\))
\(\displaystyle V=\frac{π}{3} · j · \left( R^2 + R· r + r^2 \right) + i^2 * \left(\frac{ 3 · ( r^2 + i^2 ) }{ 2· i} - i \right) \)
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