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Torus volume & surface area

modified2026-07-21statusfinished

3D geometric properties for toroidal (doughnut) rings.

[8.11] Governing equations

$$V=2\pi^2 R r^2,\quad A=4\pi^2 R r$$

Source: 1728 Software Systems.

R r
FIG. 01 — torus: major radius R (center to tube center), minor radius r (tube radius)
Volume
Surface area