Solid geometry: spheres & Platonic solids
Partial-fill volumes for spherical tanks, and complete edge/area/volume/sphere-radius properties for the five Platonic solids. (For toroidal rings, see the torus calculator.)
Spherical tank & cap volume
[8.10] Governing equations
$$V_{\text{cap}}=\frac{\pi h^2}{3}(3R-h),\quad A_{\text{cap}}=2\pi R h,\quad V_{\text{sphere}}=\frac{4}{3}\pi R^3$$
Liquid filled to depth $h$ in a sphere of radius $R$ forms a spherical cap. Source: 1728 Software Systems & Engineering ToolBox.
| Cap (liquid) volume | — | |
| Percent full | — | |
| Headspace volume | — | |
| Wetted (curved) surface area | — | |
| Full sphere volume | — | |
| Full sphere surface area | — |
Five Platonic solids
[8.12] Governing equations
$$V_{\text{tetra}}=\frac{a^3}{6\sqrt2},\quad V_{\text{cube}}=a^3,\quad V_{\text{dodec}}=\frac{15+7\sqrt5}{4}a^3$$
Surface area, volume, insphere radius $r_{\text{in}}$ and circumsphere radius $R$ of a regular solid from its edge length $a$. Source: 1728 Software Systems.
| Surface area | — | |
| Volume | — | |
| Insphere radius r_in | — | |
| Circumsphere radius R | — |