Circles — From circumference to area

Unrolling progress

Mode

Radius r

A radius joins the center to the circle. The diameter is twice the radius.

Unroll the circle, then compare its length with three diameters.

Circumference

C ≈ 18.84 cm

Approximate calculation with π ≈ 3.14

C = d × π = 2 × r × π

Circumference is the length of the boundary, measured in cm.

Diameter d = 6 cm

C / d = π ≈ 3.14

The circumference is always a little longer than three diameters, regardless of the radius.

Model notes

The model uses ideal plane geometry, with no thickness or material lost when cutting.
Geometry uses π. Decimal results are approximate calculations with π ≈ 3.14, rather than rounding calculations made with all available digits of π.
cm and cm² are model units. The drawing fits the view and is not a ruler measurement on the screen.
With 8, 16, 32 or 64 sectors, the strip still has curved and slanted edges; the dashed rectangle is only a reference.
Unrolling the boundary preserves length. Sectors only rotate and translate during rearrangement, preserving their total area.

Mathematics

Circles — From circumference to area

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