A lighthouse emits a light that can be seen for 60 miles in all direct

Question

A lighthouse emits a light that can be seen for 60 miles in all directions. If the intensity of the light is strengthened so that its visibility is increased by 40 miles in all directions, by approximately how many square miles is its region of visibility increased?

A) 6,300
B) 10,000
C) 10,300
D) 20,000
E) 31,400

Kudos if you like the question please, thanks!

A) 6,300
 B) 10,000
 C) 10,300
 D) 20,000
 E) 31,400

EgmatQuantExpert · Accepted Answer

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

vaibhav1221 · Answer

radius =  60  miles
area =  3600π

radius (extended) =  100  miles
area  10000π

Increased area = 6400π  square miles

π = \frac{22}{7}  
 6300*\frac{22}{7} = 19800 . Approx  20000 . 
D is correct

bangu · Answer

I guess you meant 6400 and not 6300 in the end.
It is 6400*22/7 = 20114
Your Answer is correct.

vaibhav1221 · Answer

Hi! 
I wrote 6300 intentionally, because, 6300 is divisble by 7. Finding an approximate answer is much faster than calculating the exact answer, which the question doesn't ask for.

Regards, 
V

Posted from my mobile device

gmatzpractice · Answer

eazy peazy pie 
pi 60^2
pi 100^2

10,000 pi - 3,600 pi

6,700 pi

Answer D

chetan2u · Answer

So its a circle of radius 60 and (60+40)=100...See attached figure

we have to find area outside the inner circle and within the outer circle

so  \pi*100^2-\pi*60^2=\pi*(100^2-60^2)=\pi(100-60)(100+60)=\pi*40*160=\pi*6400 = \frac{22}{7}*6400 ~22*900=19800 ~20000

D

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A lighthouse emits a light that can be seen for 60 miles in all direct

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