Edexcel P1 2023 June — Question 5

Exam BoardEdexcel
ModuleP1 (Pure Mathematics 1)
Year2023
SessionJune
TopicRadians, Arc Length and Sector Area

5. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{a5a5dd8b-1438-4698-929a-c5e3d5ed0694-10_488_784_310_667} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows the plan for a garden.
In the plan
  • \(O A\) and \(C D\) are perpendicular to \(O D\)
  • \(A B\) is an arc of the circle with centre \(O\) and radius 4 metres
  • \(\quad B C\) is parallel to \(O D\)
  • \(O D\) is 6 metres, \(O A\) is 4 metres and \(C D\) is 1.5 metres
    1. Show that angle \(A O B\) is 1.186 radians to 4 significant figures.
    2. Find the perimeter of the garden, giving your answer in metres to 3 significant figures.
    3. Find the area of the garden, giving your answer in square metres to 3 significant figures.