OCR C2 2014 June — Question 3

Exam BoardOCR
ModuleC2 (Core Mathematics 2)
Year2014
SessionJune
TopicRadians, Arc Length and Sector Area

3
\includegraphics[max width=\textwidth, alt={}, center]{9e95415c-00f5-4b52-a443-0b946602b3b4-2_350_597_1695_735} The diagram shows a sector \(O A B\) of a circle, centre \(O\) and radius 12 cm . The angle \(A O B\) is \(\frac { 2 } { 3 } \pi\) radians.
  1. Find the exact length of the \(\operatorname { arc } A B\).
  2. Find the exact area of the shaded segment enclosed by the arc \(A B\) and the chord \(A B\).