8.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{3cf69966-e825-4ff0-a6e8-c5dfdc92c53f-22_922_876_246_539}
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\caption{Figure 3}
\end{figure}
Figure 3 shows a sketch of the outline of the face of a ceiling fan viewed from below.
The fan consists of three identical sections congruent to \(O A B C D O\), shown in Figure 3, where
- \(O A B O\) is a sector of a circle with centre \(O\) and radius 9 cm
- \(O B C D O\) is a sector of a circle with centre \(O\) and radius 84 cm
- angle \(A O D = \frac { 2 \pi } { 3 }\) radians
Given that the length of the arc \(A B\) is 15 cm ,
- show that the length of the arc \(C D\) is 35.9 cm to one decimal place.
The face of the fan is modelled to be a flat surface.
Find, according to the model, - the perimeter of the face of the fan, giving your answer to the nearest cm,
- the surface area of the face of the fan.
Give your answer to 3 significant figures and make your units clear.