Answer
Area of the sector = 286.48 $m^{2}$
Work Step by Step
Given-
Area of the circle =600 $m^{2}$
Let radius be 'r' m
Therefore Area of the circle = $\pi r^{2}$ = 600
or $r^{2}$ = $\frac{600}{\pi}$
Now we need to calculate the area 'A' of a circular sector of this circle that subtends a central angle of 3 rad. We know that-
Area of sector, A = $\frac{1}{2} r^{2} \theta$
or
A = $\frac{1}{2}\times r^{2}\times \theta$
or
A = $\frac{1}{2}\times \frac{600}{\pi}\times 3$
(substituting for $r^{2}$ and $\theta$)
A = $\frac{900}{\pi}$ = 286.48 $m^{2}$
Therefore, area of the sector, A = 286.48 $m^{2}$
