OCR H240/01 — Question 4

Exam BoardOCR
ModuleH240/01 (Pure Mathematics)
TopicRadians, Arc Length and Sector Area

4 The diagram shows a sector \(A O B\) of a circle with centre \(O\) and radius \(r \mathrm {~cm}\).
\includegraphics[max width=\textwidth, alt={}, center]{6c16d9e2-7698-48e4-a3ed-5aae3b6f041e-05_510_606_1745_274} The angle \(A O B\) is \(\theta\) radians. The arc length \(A B\) is 15 cm and the area of the sector is \(45 \mathrm {~cm} ^ { 2 }\).
  1. Find the values of \(r\) and \(\theta\).
  2. Find the area of the segment bounded by the arc \(A B\) and the chord \(A B\).