| Exam Board | SPS |
|---|---|
| Module | SPS SM Pure (SPS SM Pure) |
| Year | 2021 |
| Session | June |
| Marks | 5 |
| Topic | Radians, Arc Length and Sector Area |
| Type | Compound shape area |
| Difficulty | Moderate -0.8 This is a straightforward application of standard arc length and sector area formulas. Part (a) uses s=rθ directly to find OD, then part (b) uses the sector area formula after finding OB and angle AOB. Both parts require only routine recall and simple arithmetic with no problem-solving insight needed. |
| Spec | 1.05d Radians: arc length s=r*theta and sector area A=1/2 r^2 theta |
\includegraphics{figure_1}
The shape $ABCDOA$, as shown in Figure 1, consists of a sector $COD$ of a circle centre $O$ joined to a sector $AOB$ of a different circle, also centre $O$.
Given that arc length $CD = 3$ cm, $\angle COD = 0.4$ radians and $AOD$ is a straight line of length 12 cm,
\begin{enumerate}[label=(\alph*)]
\item find the length of $OD$, [2]
\item find the area of the shaded sector $AOB$. [3]
\end{enumerate}
\hfill \mbox{\textit{SPS SPS SM Pure 2021 Q3 [5]}}