8
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{3836b0e7-95e6-4634-bb1e-c99b7ae3c8ba-3_378_467_269_840}
\captionsetup{labelformat=empty}
\caption{Fig. 1}
\end{figure}
Fig. 1 shows a sector \(A O B\) of a circle, centre \(O\) and radius \(O A\). The angle \(A O B\) is 1.2 radians and the area of the sector is \(60 \mathrm {~cm} ^ { 2 }\).
- Find the perimeter of the sector.
A pattern on a T-shirt, the start of which is shown in Fig. 2, consists of a sequence of similar sectors. The first sector in the pattern is sector \(A O B\) from Fig. 1, and the area of each successive sector is \(\frac { 3 } { 5 }\) of the area of the previous one.
\begin{figure}[h]
\includegraphics[alt={},max width=\textwidth]{3836b0e7-95e6-4634-bb1e-c99b7ae3c8ba-3_362_1011_1263_568}
\captionsetup{labelformat=empty}
\caption{Fig. 2}
\end{figure} - (a) Find the area of the fifth sector in the pattern.
(b) Find the total area of the first ten sectors in the pattern.
(c) Explain why the total area will never exceed a certain limit, no matter how many sectors are used, and state the value of this limit.