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Unrolling a curved ring into a rectangle is an approximation because the ring has finite thickness. A curved strip of finite width is not exactly identical to a straight rectangle; the outer and inner circumferences differ.

Conditions: The ring has a finite width $\Delta r$.; The approximation replaces a curved annulus with a straight rectangle.

Unrolling a curved ring into a rectangle is an approximation because the ring has finite thickness. A curved strip of finite width is not exactly identical to a straight rectangle; the outer and inner circumferences differ.

Conditions: The ring has a finite width $\Delta r$.; The approximation replaces a curved annulus with a straight rectangle.