Recovering and then testing a design
8 written marks
A proper sector has area \(84\text{ cm}^2\) and arc length \(21\) cm.
Part a · 3 marks
Find its radius and central angle.
Part b · 2 marks
Find its perimeter and the fraction of its full disk that it occupies.
Part c · 3 marks
A second proper sector is proposed with the same area but twice this arc length. Determine whether such a sector exists, explaining your conclusion.
Complete-answer checking, worked solutions and indicative written criteria.
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