AQA C2 2005 June — Question 2

Exam BoardAQA
ModuleC2 (Core Mathematics 2)
Year2005
SessionJune
TopicRadians, Arc Length and Sector Area

2 The diagram shows a sector \(O A B\) of a circle with centre \(O\) and radius \(r \mathrm {~cm}\).
\includegraphics[max width=\textwidth, alt={}, center]{37627fc4-a90b-4f3b-9b10-0a9e200f8485-2_486_381_1686_739} The angle \(A O B\) is 1.5 radians. The perimeter of the sector is 56 cm .
  1. Show that \(r = 16\).
  2. Find the area of the sector.