Answer
$\frac{\pi}{4}$ sq ft
Work Step by Step
As the circles with radii 1, 2, and 3 ft are externally tangent to one another, the line segments joining the center of that circle to the centers of the other two circles will be perpendicular to each other.
Thus the central angle of the said sector will be of 90 degrees, i.e.
$\theta$ = 90 degrees = $90\times\frac{\pi}{180}$ = $\frac{\pi}{2}$ rad
Given, r = 1 ft
We know that area 'A' of a circular sector with central angle $\theta$ rad and radius 'r' is given by-
A = $\frac{1}{2} r^{2} \theta$
= $\frac{1}{2} \times1^{2} \times\frac{\pi}{2}$
= $\frac{\pi}{4}$ sq ft
