Edexcel C2 2006 June — Question 8

Exam BoardEdexcel
ModuleC2 (Core Mathematics 2)
Year2006
SessionJune
TopicRadians, Arc Length and Sector Area

8. \begin{figure}[h]
\captionsetup{labelformat=empty} \caption{Figure 2} \includegraphics[alt={},max width=\textwidth]{29c7baa1-6929-448a-a756-319ea75dffa7-10_620_636_301_660}
\end{figure} Figure 2 shows the cross section \(A B C D\) of a small shed. The straight line \(A B\) is vertical and has length 2.12 m . The straight line \(A D\) is horizontal and has length 1.86 m . The curve \(B C\) is an arc of a circle with centre \(A\), and \(C D\) is a straight line. Given that the size of \(\angle B A C\) is 0.65 radians, find
  1. the length of the arc \(B C\), in m , to 2 decimal places,
  2. the area of the sector \(B A C\), in \(\mathrm { m } ^ { 2 }\), to 2 decimal places,
  3. the size of \(\angle C A D\), in radians, to 2 decimal places,
  4. the area of the cross section \(A B C D\) of the shed, in \(\mathrm { m } ^ { 2 }\), to 2 decimal places.