CAIE P1 2013 November — Question 6

Exam BoardCAIE
ModuleP1 (Pure Mathematics 1)
Year2013
SessionNovember
TopicArea Under & Between Curves

6
\includegraphics[max width=\textwidth, alt={}, center]{16a5835e-002f-4c49-aacf-cda41c37f214-3_463_621_255_762} The diagram shows sector \(O A B\) with centre \(O\) and radius 11 cm . Angle \(A O B = \alpha\) radians. Points \(C\) and \(D\) lie on \(O A\) and \(O B\) respectively. Arc \(C D\) has centre \(O\) and radius 5 cm .
  1. The area of the shaded region \(A B D C\) is equal to \(k\) times the area of the unshaded region \(O C D\). Find \(k\).
  2. The perimeter of the shaded region \(A B D C\) is equal to twice the perimeter of the unshaded region \(O C D\). Find the exact value of \(\alpha\).