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

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A lighthouse emits a light that can be seen for 60 miles in all direct  [#permalink]

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New post 12 Jul 2018, 19:40
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A
B
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D
E

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Question Stats:

67% (01:16) correct 33% (02:05) wrong based on 45 sessions

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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!

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Re: A lighthouse emits a light that can be seen for 60 miles in all direct  [#permalink]

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New post 12 Jul 2018, 20:27
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
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Re: A lighthouse emits a light that can be seen for 60 miles in all direct  [#permalink]

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New post 12 Jul 2018, 20:50
vaibhav1221 wrote:
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

I guess you meant 6400 and not 6300 in the end.
It is 6400*22/7 = 20114
Your Answer is correct.
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Re: A lighthouse emits a light that can be seen for 60 miles in all direct  [#permalink]

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New post 13 Jul 2018, 05:14
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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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Re: A lighthouse emits a light that can be seen for 60 miles in all direct  [#permalink]

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New post 13 Jul 2018, 19:30
bangu wrote:
vaibhav1221 wrote:
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

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


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
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Regards,

Vaibhav



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~GMAC

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Re: A lighthouse emits a light that can be seen for 60 miles in all direct  [#permalink]

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New post 13 Jul 2018, 19:41
eazy peazy pie
pi 60^2
pi 100^2

10,000 pi - 3,600 pi

6,700 pi

Answer D
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A lighthouse emits a light that can be seen for 60 miles in all direct  [#permalink]

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New post 13 Jul 2018, 20:00
Carlgrc wrote:
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!



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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