AQA C2 2013 June — Question 2

Exam BoardAQA
ModuleC2 (Core Mathematics 2)
Year2013
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]{f4f090a1-7e36-4993-a49e-b6e7e8589057-2_341_371_968_815} The radius of the circle is 20 cm and the angle \(A O B = 0.8\) radians.
  1. Find the length of the arc \(A B\).
  2. Find the area of the sector \(O A B\).
  3. A line from \(B\) meets the radius \(O A\) at the point \(D\), as shown in the diagram below.
    \includegraphics[max width=\textwidth, alt={}, center]{f4f090a1-7e36-4993-a49e-b6e7e8589057-2_344_371_1747_815} The length of \(B D\) is 15 cm . Find the size of the obtuse angle \(O D B\), in radians, giving your answer to three significant figures.