OCR MEI C2 2011 June — Question 13

Exam BoardOCR MEI
ModuleC2 (Core Mathematics 2)
Year2011
SessionJune
TopicRadians, Arc Length and Sector Area

13 Fig. 13.1 shows a greenhouse which is built against a wall. \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{97ed9d1d-b9e5-47d6-a451-b14757c0e19d-4_606_828_347_358} \captionsetup{labelformat=empty} \caption{Fig. 13.1}
\end{figure} \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{97ed9d1d-b9e5-47d6-a451-b14757c0e19d-4_401_350_529_1430} \captionsetup{labelformat=empty} \caption{Fig. 13.2}
\end{figure} The greenhouse is a prism of length 5.5 m . The curve AC is an arc of a circle with centre B and radius 2.1 m , as shown in Fig. 13.2. The sector angle ABC is 1.8 radians and ABD is a straight line. The curved surface of the greenhouse is covered in polythene.
  1. Find the length of the arc AC and hence find the area of polythene required for the curved surface of the greenhouse.
  2. Calculate the length BD .
  3. Calculate the volume of the greenhouse.