AQA C2 2011 January — Question 1

Exam BoardAQA
ModuleC2 (Core Mathematics 2)
Year2011
SessionJanuary
TopicRadians, Arc Length and Sector Area

1 The diagram shows a sector \(O A B\) of a circle with centre \(O\) and radius 5 cm .
\includegraphics[max width=\textwidth, alt={}, center]{1c06ba04-575c-4eb8-b4aa-0a7510838cd2-02_415_525_550_794} The angle between the radii \(O A\) and \(O B\) is \(\theta\) radians.
The length of the \(\operatorname { arc } A B\) is 4 cm .
  1. Find the value of \(\theta\).
  2. Find the area of the sector \(O A B\).