Answer
Radius, r $\approx 5.53$ m
Work Step by Step
Given-
Central angle of the sector. $\theta$ = $\frac{5\pi}{12}$ rad
radius, r = ?
A =20 $m^{2}$
We know that area 'A' of a circular sector with central angle $\theta$ rad and radius 'r' is given by-
A = $\frac{1}{2} r^{2} \theta$
or
20 = $\frac{1}{2}\times r^{2}\times \frac{5\pi}{12}$
or
20 = $\frac{5\pi r^{2}}{24}$
or
$5\pi r^{2}$ = $ 20\times24$
or
$ r^{2}$ = $\frac{20\times24}{5\pi}$ = $\frac{96}{\pi}$ = $\frac{96}{3.14}$ = 30.57
Therefore, r= $\sqrt {30.57}\approx 5.53$ m
