Question 11 - A-Level Maths

Exam Board	OCR MEI
Module	C2 (Core Mathematics 2)
Year	2009
Session	January
Topic	Radians, Arc Length and Sector Area

\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{838d6b15-69a9-4e67-bc36-5bf60254a767-5_469_878_274_671} \captionsetup{labelformat=empty} \caption{Fig. 11.1}
\end{figure} Fig. 11.1 shows the surface ABCD of a TV presenter's desk. AB and CD are arcs of circles with centre O and sector angle 2.5 radians. \(\mathrm { OC } = 60 \mathrm {~cm}\) and \(\mathrm { OB } = 140 \mathrm {~cm}\).
(A) Calculate the length of the arc CD.
(B) Calculate the area of the surface ABCD of the desk.
The TV presenter is at point P , shown in Fig. 11.2. A TV camera can move along the track EF , which is of length 3.5 m . \begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{838d6b15-69a9-4e67-bc36-5bf60254a767-5_378_877_1334_675} \captionsetup{labelformat=empty} \caption{Fig. 11.2}
\end{figure} When the camera is at E , the TV presenter is 1.6 m away. When the camera is at F , the TV presenter is 2.8 m away.
(A) Calculate, in degrees, the size of angle EFP.
(B) Calculate the shortest possible distance between the camera and the TV presenter.