The area of a quadrant of a circle is $\frac{\pi}{9} m^2$. Its radius (in metres) is equal to:

$\frac{2}{3}$

We know that,

The area of a quadrant of a circle is equal to one-fourth of the area of the circle = \(\frac{πr^2}{4}\) 

Area of a quadrant of a circle is = $\frac{\pi}{9} m^2$

So,

\(\frac{πr^2}{4}\) = \(\frac{π}{9}\) 

= r² = \(\frac{4}{9}\) 

= r = \(\frac{2}{3}\) 

$\frac{\pi}{9} m^2$