Solution

Given: A lighthouse emits a light that can be seen for 60 miles in all directions

When the intensity of the light is increased, the visibility of light is increased by 40 miles in all directions

To find: How many square miles is its region of visibility increased?

Approach and Working: When emitted light can be seen up to 60 miles in all directions:

Area covered= \(π* (60)^2= 3600 π\) miles

When intensity of light is increased further 40 miles:

Now, the light can be seen in 60+40= 100 miles

Area covered= \(π* (100)^2= 10000 π\) miles

Hence, increase in area= \(10000 π- 3600 π= 6400 π\)= 6400*3.14 ≈ 20,000

Hence, the correct answer is option D.

Answer: D
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