Volume of a truncated right circular cone
Calculates the volume, base area, lateral surface area, and cut-face area of the portion of a right circular cone cut by a vertical plane, using its radius and height.
| Volume V | |
| Base Area SB | |
| Lateral Surface Area SL | |
| Cross-sectional Area Sh | |
| Central angle θ | rad |
| Arc Length L | |
| Chord length c |
| \( \normalsize Partial\ Circular\ Cone\\ \hspace{130px} k=1-{\large\frac{a}{r}}\\ (1)\ center\ angle:\hspace{8px} \theta=2\cos^{\tiny-1}k\\ (2)\ circular\ arc :\ L=r\theta\\ (3)\ chord :\hspace{60px} c=2r\sqrt{1-k^2}\\ (4)\ area:\\ \hspace{30px} S_B={\large\frac{\theta}{2}}r^{2}-rk{\large\frac{c}{2}}\\ \hspace{30px} S_L=r\sqrt{r^2+h^2}\left\{{\large\frac{\pi}{2}}-\sin^{\tiny-1}k-k\sqrt{1-k^2}\right\}\\ \hspace{30px} S_h=hr\left\{\sqrt{1-k^2}-k^2\cosh^{\tiny-1}{\large\frac{1}{k}}\right\}\\ (5)\ volume:\\ \hspace{30px} V={\large\frac{hr^2}{3}}\left\{{\large\frac{\pi}{2}}-2k\sqrt{1-k^2}-\sin^{\tiny-1}k+k^3\cosh^{\tiny-1}{\large\frac{1}{k}}\right\}\\ \) |
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