\includegraphics{figure_1}
Figure 1 shows a sketch of a segment \(PQRP\) of a circle with centre \(O\) and radius \(5\) cm.
Given that
• angle \(PQR\) is \(\theta\) radians
• \(\theta\) is increasing, from \(0\) to \(\pi\), at a constant rate of \(0.1\) radians per second
• the area of the segment \(PQRP\) is \(A\) cm²
- show that
$$\frac{dA}{d\theta} = K(1 - \cos \theta)$$
where \(K\) is a constant to be found.
[2]
- Find, in cm²s⁻¹, the rate of increase of the area of the segment when \(\theta = \frac{\pi}{3}\)
[4]