1 The diagram shows a sector \(O A B\) of a circle with centre \(O\).
\includegraphics[max width=\textwidth, alt={}, center]{961ff4d6-b62a-4fab-8204-8a33a969d343-2_444_373_541_804}
The radius of the circle is 15 cm and angle \(A O B = 1.2\) radians.
- Show that the area of the sector is \(135 \mathrm {~cm} ^ { 2 }\).
- Calculate the length of the arc \(A B\).
- The point \(P\) lies on the radius \(O B\) such that \(O P = 10 \mathrm {~cm}\), as shown in the diagram below.
\includegraphics[max width=\textwidth, alt={}, center]{961ff4d6-b62a-4fab-8204-8a33a969d343-2_449_378_1436_799}
Calculate the perimeter of the shaded region bounded by \(A P , P B\) and the arc \(A B\), giving your answer to three significant figures.
(5 marks)