A search plane carries radar equipment that can detect metal objects (like submarine periscopes or plane wreckage) on the ocean surface up to 15.5 miles away. If the plane completes a circular flight pattern of 471 miles in circumference, how much area will it search?

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26-04-2022
Mathematics

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A search plane carries radar equipment that can detect metal objects (like submarine periscopes or plane wreckage) on the ocean surface up to 15.5 miles away. If the plane completes a circular flight pattern of 471 miles in circumference, how much area will it search?

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astha8579 astha8579 · Answer 1 · 2022-05-03T11:02:52+02:00

The area that the considered search plane searches with the given figures is 16957.42 miles² approximately.

How to find the area of a circle?

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

How are radius and circumference of a circle related?

Suppose that a considered circle has:

Circumference = C units
Radius = r units

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:

Area of internal circle = [tex]\pi r^2 = \pi \times \left( \dfrac{471}{2\pi} \right)^2 \approx 17,653.56 \: \rm miles ^2[/tex]
Area of outer circle = [tex]\pi \times \left( \dfrac{471}{2\pi} + 30 \right )^2 \approx 34610.98 \: \rm miles ^2[/tex]

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:

https://brainly.com/question/13004063

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