Edexcel C12 2017 October — Question 8

Exam BoardEdexcel
ModuleC12 (Core Mathematics 1 & 2)
Year2017
SessionOctober
TopicRadians, Arc Length and Sector Area

8. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{bb1becd5-96c1-426d-9b85-4bbc4a61af27-18_387_397_255_794} \captionsetup{labelformat=empty} \caption{Figure 3}
\end{figure} Figure 3 shows a circle with centre \(O\) and radius \(r \mathrm {~cm}\). The points \(A\) and \(B\) lie on the circumference of this circle. The minor arc \(A B\) subtends an angle \(\theta\) radians at \(O\), as shown in Figure 3.
Given the length of minor \(\operatorname { arc } A B\) is 6 cm and the area of minor sector \(O A B\) is \(20 \mathrm {~cm} ^ { 2 }\),
  1. write down two different equations in \(r\) and \(\theta\).
  2. Hence find the value of \(r\) and the value of \(\theta\).