#### Answer

4.5 cm

#### Work Step by Step

Given that the exact area of the sector determined by 40$^{\circ}$ arc is $\frac{9}{4}\pi cm^{2}$
We need to find the length of the radius of the circle
In circle of radius length r, the area A of a sector whose arc has degree m is A = $\frac{m}{360} \pi r^{2}$
$\frac{9}{4}\pi$ = $\frac{40}{360} \pi r^{2}$
$r^{2}$ = $\frac{81}{4}$
r = $\sqrt \frac{81}{4}$
r = $\frac{9}{2}$ = 4.5 cm
The radius of the circle = 4.5 cm