# Volume of a partial circular cone Calculator

## Calculates the volume and the bottom, lateral and cross-section areas of a partial circular cone given the radius of cone, height of partial cone and the height of arch.

radius of cone r
height of a partial cone h
height of arch a
1. ≦r

volume V
bottom area SB
lateral area SL
cross-section area Sh
center angle θ
circular arc L
chord c
 $\normal Partial\ Circular\ Cone\\\hspace{130} k=1-{\large\frac{a}{r}}\\(1)\ center\ angle:\hspace{8} \theta=2\cos^{\tiny-1}k\\(2)\ circular\ arc :\ L=r\theta\\(3)\ chord :\hspace{60} c=2r\sqrt{1-k^2}\\(4)\ area:\\\hspace{30} S_B={\large\frac{\theta}{2}}r^{2}-rk{\large\frac{c}{2}}\\\hspace{30} S_L=r\sqrt{r^2+h^2}\left{{\large\frac{\pi}{2}}-\sin^{\tiny-1}k-k\sqrt{1-k^2}\right}\\\hspace{30} S_h=hr\left{\sqrt{1-k^2}-k^2\cosh^{\tiny-1}{\large\frac{1}{k}\right}\\(5)\ volume:\\\hspace{30} V={\large\frac{hr^2}{3}}\left{{\large\frac{\pi}{2}}-2k\sqrt{1-k^2}-\sin^{\tiny-1}k+k^3\cosh^{\tiny-1}{\large\frac{1}{k}\right}\\$

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