Edexcel C12 2015 June — Question 7

Exam BoardEdexcel
ModuleC12 (Core Mathematics 1 & 2)
Year2015
SessionJune
TopicRadians, Arc Length and Sector Area

7. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{ea81408b-e292-4529-b1e2-e3246503a3ac-09_440_437_285_772} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows a circle with centre \(O\) and radius 9 cm . The points \(A\) and \(B\) lie on the circumference of this circle. The minor sector \(O A B\) has perimeter 30 cm and the angle between the radii \(O A\) and \(O B\) of this sector is \(\theta\) radians. Find
  1. the length of the arc \(A B\),
  2. the value of \(\theta\),
  3. the area of the minor sector \(O A B\),
  4. the area of triangle \(O A B\), giving your answer to 3 significant figures.