Answer:
The beam from the lighthouse covers a circular area, and we are given that the maximum distance at which the beam is visible is 3 miles. This means that the radius of the circle is 3 miles.
To find the area of the circle covered by the beam as it sweeps in an arc of 150°, we need to calculate what fraction of the circle's total area corresponds to this arc. To do this, we can use the formula:
fraction of circle's area = (central angle of arc / 360°)
In this case, the central angle of the arc is 150°, so the fraction of the circle's area covered by the arc is:
fraction of circle's area = 150° / 360°
fraction of circle's area = 5/12
Therefore, the area covered by the beam is:
area = fraction of circle's area x total area of circle
area = (5/12) x π x radius^2
area = (5/12) x π x 3^2
area = 3.93 square miles (rounded to the nearest square mile)
Therefore, the area covered by the beam as it sweeps in an arc of 150° is approximately 3.93 square miles.
Simple explanation:
The area covered by the beam from the lighthouse as it sweeps in an arc of 150° is approximately 3.93 square miles (rounded to the nearest square mile).
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