E-CB01 · Recovering a curved strip
An annular sector has radial width \(3\) cm, angle \(1.2\) rad and area \(27\text{ cm}^2\). Its outer and inner radii are \(R\) and \(r\).
Find \(R+r\), then determine both radii.
Find its complete perimeter.
A complete annulus is made using the same radii, with no slit. Find its area and total boundary length, and explain why putting \(\theta=2\pi\) into the cut-sector perimeter formula gives a wrong answer.
Complete-answer checking, worked solutions and indicative written criteria.
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