The area that the considered search plane searches with the given figures is 16957.42 miles² approximately.
Suppose the circle has radius of 'r' units, then, its area is given as:
[tex]A = \pi \times r^2[/tex] sq. units
Since radius of a circle is half of its diameter, so if diameter is of 'd' length, then r= d/2, thus, area can be rewritten as:
[tex]\pi \times (\dfrac{d}{2})^2[/tex] sq. units
Suppose that a considered circle has:
Then, we get:
[tex]C = 2\pi r \: \rm units[/tex]
So, the radar scans the surface of ocean in a circular area with radius of 15.5 miles.
That circular area is itself moved in a circular path (due to circular motion of the plane with 471 miles circumference of the circular path).
The graph given describes the region of scan.
The blue region's area = Outer circle's area - Internal circle's area
The Internal circle has circumference 471 miles, let its radius be 'r' miles, then:
[tex]471 = 2\pi r\\\\r = \dfrac{471}{2\pi} \: \rm miles[/tex]
The outer circle has the radius = internal circle's radius + diameter of the radar circle = [tex]\dfrac{471}{2\pi} + 2(15.5) =\dfrac{471}{2\pi} + 30 \: \rm miles[/tex]
Thus, we get:
Net area which is searched by the search plane ≈ 34610.98 - 17653.56 miles²
Net area which is searched by the search plane ≈ 16957.42 miles²
Thus, the area that the considered search plane searches with the given figures is 16957.42 miles² approximately.
Learn more about area of a circle here:
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