CAIE P1 2023 June — Question 6

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2023
SessionJune
TopicCircles

6
\includegraphics[max width=\textwidth, alt={}, center]{51bd3ba6-e1d1-4c07-81cd-d99dd77f9306-07_389_552_267_799} The diagram shows a sector \(O A B\) of a circle with centre \(O\) and radius \(r \mathrm {~cm}\). Angle \(A O B = \theta\) radians. It is given that the length of the \(\operatorname { arc } A B\) is 9.6 cm and that the area of the sector \(O A B\) is \(76.8 \mathrm {~cm} ^ { 2 }\).
  1. Find the area of the shaded region.
  2. Find the perimeter of the shaded region.