Edexcel C2 — Question 7

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

7. \begin{figure}[h]
\captionsetup{labelformat=empty} \caption{Figure 1} \includegraphics[alt={},max width=\textwidth]{ba5cb933-dedd-4ad9-9e66-49636870b3de-3_739_1272_826_328}
\end{figure} Fig. 1 shows the cross-section \(A B C D\) of a chocolate bar, where \(A B , C D\) and \(A D\) are straight lines and \(M\) is the mid-point of \(A D\). The length \(A D\) is 28 mm , and \(B C\) is an arc of a circle with centre \(M\). Taking \(A\) as the origin, \(B , C\) and \(D\) have coordinates (7,24), (21,24) and (28,0) respectively.
  1. Show that the length of \(B M\) is 25 mm .
  2. Show that, to 3 significant figures, \(\angle B M C = 0.568\) radians.
  3. Hence calculate, in \(\mathrm { mm } ^ { 2 }\), the area of the cross-section of the chocolate bar. Given that this chocolate bar has length 85 mm ,
  4. calculate, to the nearest \(\mathrm { cm } ^ { 3 }\), the volume of the bar.