Figure 1 shows the sector $AOB$ of a circle with centre $O$ and radius $3r$ cm

A circle with radius $r$ cm touches $OA$ and $OB$ and the arc $AB$

Angle $AOB$is $\theta$ radians, where $0< \theta <\frac{ \pi }{2}$

Find the exact value of $\theta$

1.2. The area of the region shown shaded in Figure 1 is $8 \pi$ cm²

Find the value of $r$