# Volume of a truncated circular cone not a frustum Calculator

## Calculates the volume, upper and bottom areas of a truncated circular cone that is not a frustum.

cone height H
angle θ
 degree
 (θ:cutting plane angle with flat base)

volume V
cutting area Su
bottom area SB
 $\normal Truncated\ cone\ not\ a\ frustum\\(1)\hspace{10} k={\large\frac{H}{R}},\ m=\tan{\theta}\\\hspace{25}R:r=H:h+rm\hspace{10}\rightarrow\ h=r*(k-m)\\(2)\ elliptical\ radius :\\\hspace{95} a={\large\frac{hk}{k^2-m^2}}\sec\theta\\\hspace{95} b={\large\frac{h}{sqrt{k^2-m^2}}}\\(3)\ area:\hspace{30} S_B=\pi R^2\\\hspace{95} S_u=\pi ab\\(4)\ volume:\hspace{10} V_{cap}={\large\frac{\pi k}{3}}\left{\large\frac{h}{sqrt{k^2-m^2}}\right}^3\\\hspace{95} V={\large\frac{\pi}{3}}R^2H-V_{cap}\\$

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