Edexcel PMT Mocks — Question 2

Exam BoardEdexcel
ModulePMT Mocks (PMT Mocks)
TopicRadians, Arc Length and Sector Area

2. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{63d85737-99d4-4916-a479-fe44f77b1505-03_442_552_351_721} \captionsetup{labelformat=empty} \caption{Figure 1}
\end{figure} Figure 1 shows a sector \(P O Q\) of a circle with centre \(O\) and radius \(r \mathrm {~cm}\).
The angle \(P O Q\) is 0.5 radians.
The area of the sector is \(9 \mathrm {~cm} ^ { 2 }\).
Show that the perimeter of the sector is \(k\) times the length of the arc, where \(k\) is an integer.