Answer
Radius $\approx 7.57$ m
Work Step by Step
Given-
Central angle of the sector. $\theta$ = $140^{\circ}$
or, $\theta$ = $140\times\frac{\pi}{180}$ = $\frac{7\pi}{9}$ rad
radius, r = ?
A =70 $m^{2}$
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
70 = $\frac{1}{2}\times r^{2}\times \frac{7\pi}{9}$
or
70 = $\frac{7\pi r^{2}}{18}$
or
$7\pi r^{2}$ = $ 70\times18$
or
$ r^{2}$ = $\frac{70\times18}{7\pi}$ = $\frac{180}{\pi}$ = $\frac{180}{3.14}$ = 57.33
Therefore, r= $\sqrt {57.33}\approx 7.57$ m
