1.69: Circular measure and sectors and areas using trigonometry

Figure 1 shows a sector of a circle. The circle has radius $r$ cm and the sector has angle $\theta$ radians. The sector has an arc length of $18\pi$ cm and an area of $126\pi\text{ cm}^2$.

Find

(i) the value of $r$,

(ii) the exact value of $\theta$. (5)