# 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 ≦r 6dgt10dgt14dgt18dgt22dgt26dgt30dgt34dgt38dgt42dgt46dgt50dgt volume V bottom area SB lateral area SL cross-section area Sh center angle θ rad circular arc L chord c
 $\normal Partial\ Circular\ Cone\\\hspace{130} k=1-{\large\frac{a}{r}}\\(1)\ center\ angle:\hspace{8} \theta=2\cos^{\tiny-1}k\\(2)\ circular\ arc :\ L=r\theta\\(3)\ chord :\hspace{60} c=2r\sqrt{1-k^2}\\(4)\ area:\\\hspace{30} S_B={\large\frac{\theta}{2}}r^{2}-rk{\large\frac{c}{2}}\\\hspace{30} S_L=r\sqrt{r^2+h^2}\left{{\large\frac{\pi}{2}}-\sin^{\tiny-1}k-k\sqrt{1-k^2}\right}\\\hspace{30} S_h=hr\left{\sqrt{1-k^2}-k^2\cosh^{\tiny-1}{\large\frac{1}{k}\right}\\(5)\ volume:\\\hspace{30} V={\large\frac{hr^2}{3}}\left{{\large\frac{\pi}{2}}-2k\sqrt{1-k^2}-\sin^{\tiny-1}k+k^3\cosh^{\tiny-1}{\large\frac{1}{k}\right}\\$

Sending completion

To improve this 'Volume of a partial circular cone Calculator', please fill in questionnaire.
Male or Female ?
Male Female
Age
Under 20 years old 20 years old level 30 years old level
40 years old level 50 years old level 60 years old level or over
Occupation
Elementary school/ Junior high-school student
High-school/ University/ Grad student A homemaker An office worker / A public employee
Self-employed people An engineer A teacher / A researcher
A retired people Others
Useful?
Very Useful A little Not at All
Purpose of use?