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The spray from a certain water sprinkler covers a circular region of l

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Bunuel
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The spray from a certain water sprinkler covers a circular region of l [#permalink] New post   29 Nov 2020, 09:45
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66% (01:13) correct 34% (01:40) wrong based on 58 sessions
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The spray from a certain water sprinkler covers a circular region of lawn \(25\pi\) square yards in area, with the sprinkler at the center. If the water pressure to the sprinkler is increased, so that the area covered by the sprinkler is increased by 300%, how far from the sprinkler does the spray reach?

(A) \(5\sqrt{3}\)

(B) 10

(C) 15

(D) \(10\sqrt{3}\)

(E) 20
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parth2424
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The spray from a certain water sprinkler covers a circular region of l [#permalink] New post   Updated on: 29 Nov 2020, 10:42
B)
new area 100pi
R^2 = 100
R = 10

Posted from my mobile device

Originally posted by parth2424 on 29 Nov 2020, 10:19.
Last edited by parth2424 on 29 Nov 2020, 10:42, edited 1 time in total.
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Re: The spray from a certain water sprinkler covers a circular region of l [#permalink] New post   29 Nov 2020, 10:36
New Area = 25pi*4= 100pi

r=10

hence B) 10
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Re: The spray from a certain water sprinkler covers a circular region of l [#permalink] New post   29 Nov 2020, 10:37
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Bunuel wrote:
The spray from a certain water sprinkler covers a circular region of lawn \(25\pi\) square yards in area, with the sprinkler at the center. If the water pressure to the sprinkler is increased, so that the area covered by the sprinkler is increased by 300%, how far from the sprinkler does the spray reach?

(A) \(5\sqrt{3}\)

(B) 10

(C) 15

(D) \(10\sqrt{3}\)

(E) 20

New area is \(\frac{(300+100)}{100}*25\pi\) = \(100\pi\)

We know area is \(πr^2 = 100π\)

So, \(r = 10\), Answer must be (B)

parth2424 wrote:
A)
new area 75pi.
R^2 = 75
R = sqrt(5*5*3)
R = 5 sqrt 3

Posted from my mobile device
increased by 300% means to be multiplied by 4
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Re: The spray from a certain water sprinkler covers a circular region of l [#permalink] New post   29 Nov 2020, 10:44
Thanks for pointing that out :D

Abhishek009 wrote:
Bunuel wrote:
The spray from a certain water sprinkler covers a circular region of lawn \(25\pi\) square yards in area, with the sprinkler at the center. If the water pressure to the sprinkler is increased, so that the area covered by the sprinkler is increased by 300%, how far from the sprinkler does the spray reach?

(A) \(5\sqrt{3}\)

(B) 10

(C) 15

(D) \(10\sqrt{3}\)

(E) 20

New area is \(\frac{(300+100)}{100}*25\pi\) = \(100\pi\)

We know area is \(πr^2 = 100π\)

So, \(r = 10\), Answer must be (B)

parth2424 wrote:
A)
new area 75pi.
R^2 = 75
R = sqrt(5*5*3)
R = 5 sqrt 3

Posted from my mobile device
increased by 300% means to be multiplied by 4
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Re: The spray from a certain water sprinkler covers a circular region of l [#permalink] New post   30 Nov 2020, 00:56
The spray from a certain water sprinkler covers a circular region of lawn square yards in area, with the sprinkler at the center. If the water pressure to the sprinkler is increased, so that the area covered by the sprinkler is increased by 300%, how far from the sprinkler does the spray reach?

Previously Area covered = 25π
New area covered = 4*25π =100π

πr^2 = 100π
r = 10

Posted from my mobile device
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EgmatQuantExpert
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Re: The spray from a certain water sprinkler covers a circular region of l [#permalink] New post   30 Nov 2020, 22:09
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Solution


Given
In this question, we are given that
    • Area of smaller circle = 25π
    • Area covered by the sprinkler increased by 300%

To find
We need to determine
    • The radius of the bigger circle

Approach and Working out
    • Area of bigger circle = 25π + 3 x 25π = 100π
      o This implies, \(πr^2 = 100π\)
      o Thus, r = 10

Hence, Option B is the correct answer.

Correct Answer: Option B
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Re: The spray from a certain water sprinkler covers a circular region of l [#permalink]
30 Nov 2020, 22:09
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