Edexcel P1 2022 January — Question 5

Exam BoardEdexcel
ModuleP1 (Pure Mathematics 1)
Year2022
SessionJanuary
TopicRadians, Arc Length and Sector Area

5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{6c320b71-8793-461a-a078-e4f64c144a3a-12_401_677_219_635} \captionsetup{labelformat=empty} \caption{Figure 2}
\end{figure} Figure 2 shows a plan view of a semicircular garden \(A B C D E O A\) The semicircle has
  • centre \(O\)
  • diameter \(A O E\)
  • radius 3 m
The straight line \(B D\) is parallel to \(A E\) and angle \(B O A\) is 0.7 radians.
  1. Show that, to 4 significant figures, angle \(B O D\) is 1.742 radians. The flowerbed \(R\), shown shaded in Figure 2, is bounded by \(B D\) and the arc \(B C D\).
  2. Find the area of the flowerbed, giving your answer in square metres to one decimal place.
  3. Find the perimeter of the flowerbed, giving your answer in metres to one decimal place.