Final answer:
To determine the area covered by the lighthouse's light, we need the distance to the pier to use as the radius in the area formula for a circle, A = πr². Without this radius, we cannot compute the area, which is necessary to choose the correct answer from the provided options.
Step-by-step explanation:
The question concerns the area that a lighthouse's revolving beam of light would cover. To answer this question, we need to consider that the area illuminated by the lighthouse is circular, with the lighthouse at the center of this area. Since the pier is the farthest point the light reaches, the distance to the pier would be the radius of the circular area. From physics, we know that the intensity of light decreases with the square of the distance from the source, as per the inverse-square law. This knowledge, however, doesn't directly help us calculate the area, as we need the actual radius to compute the area using the formula for the area of a circle, which is A = πr², where 'A' is the area and 'r' is the radius.
For example, in astronomy, to calculate the light-collecting area of a telescope, we use the diameter to find the radius (half the diameter) and then apply the formula A = πr². A 1-m diameter telescope would have a radius of 0.5 m, yielding an area of 0.79 m², while a 4-m diameter telescope has a radius of 2 m and an area of approximately 12.6 m², which is 16 times larger than that of the 1-m telescope. This corresponds with the fact that as the radius doubles, the area increases by a factor of the square of the radius increase (—in this case, 2² = 4).
In the case of the lighthouse, without the exact measurement of the radius (the distance to the pier), we cannot determine the exact area covered by the light. Hence, unless the distance is provided, we cannot select the correct answer from the options given: A. 0.4 square miles, B. 1 square mile, C. 2.5 square miles, or D. 4 square miles. It's important to understand such concepts to solve problems related to light intensity and area in various applications, including astronomy and engineering.