SPS SPS SM Pure 2021 June — Question 3

Exam BoardSPS
ModuleSPS SM Pure (SPS SM Pure)
Year2021
SessionJune
TopicRadians, Arc Length and Sector Area

3. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{106e8e6b-912d-45ef-89e9-12ffc04bfd25-06_369_661_155_760} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} The shape \(A B C D O A\), as shown in Figure 1, consists of a sector \(C O D\) of a circle centre \(O\) joined to a sector \(A O B\) of a different circle, also centre \(O\). Given that arc length \(C D = 3 \mathrm {~cm} , \angle C O D = 0.4\) radians and \(A O D\) is a straight line of length 12 cm ,
  1. find the length of \(O D\),
  2. find the area of the shaded sector \(A O B\).