AQA C2 2011 June — Question 2

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

2 The diagram shows a sector \(O A B\) of a circle with centre \(O\).
\includegraphics[max width=\textwidth, alt={}, center]{258f0400-6e3b-406c-9f86-acc9fff4e094-2_440_392_1500_826} The radius of the circle is 6 cm and the angle \(A O B = 0.5\) radians.
  1. Find the area of the sector \(O A B\).
    1. Find the length of the arc \(A B\).
    2. Hence show that the perimeter of the sector \(O A B = k \times\) the length of the \(\operatorname { arc } A B\) where \(k\) is an integer.