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Calculate volume and surface area of a torus (donut shape). Enter major radius R and minor radius r.
Standard donut shape with a hole in the middle. Most common type.
The inner edge touches itself at a single point. No visible hole.
Self-intersecting shape. The tube overlaps with itself.
A torus is a doughnut-shaped surface created by rotating a circle around an axis that doesn't intersect the circle. It's topologically distinct from a sphere.
The torus is generated by two rotations: the circle of radius r rotates around the axis, and R is the radius of that rotation. Each rotation contributes a factor of π.
Donuts, bagels, inner tubes, O-rings, lifebuoys, some furniture cushions, and tokamak fusion reactors all have torus shapes.
The Euler characteristic χ = 0 (compared to 2 for a sphere). A torus has 1 hole (genus = 1), making it topologically equivalent to a coffee mug with a handle.