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A circular swimming pool is surrounded by a wall with a height of 2m.

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A circular swimming pool is surrounded by a wall with a height of 2m.  [#permalink]

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New post Updated on: 23 May 2020, 08:58
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[GMAT math practice question]

A circular swimming pool is surrounded by a walk with a width of 2m. The area of the walk is 21% of the area of the swimming pool. What is the area of the swimming pool?

A. \(400π\) \(m^2\)
B. \(300π\) \(m^2\)
C. \(250π\) \(m^2\)
D. \(200π\) \(m^2\)
E. \(100π\) \(m^2\)

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Originally posted by MathRevolution on 22 May 2020, 05:28.
Last edited by MathRevolution on 23 May 2020, 08:58, edited 1 time in total.
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Re: A circular swimming pool is surrounded by a wall with a height of 2m.  [#permalink]

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New post 22 May 2020, 05:43
Sir, kindly check the height of wall. Are you sure it's not 1m?
Because the last value I m getting for r(h+r)=42
And if h is 2, r will be of some imaginary value.
Kindly revert.

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Re: A circular swimming pool is surrounded by a wall with a height of 2m.  [#permalink]

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New post 22 May 2020, 07:44
MathRevolution wrote:
[GMAT math practice question]

A circular swimming pool is surrounded by a wall with a height of 2m. The area of the wall is 21% of the area of the swimming pool. What is the area of the swimming pool?

A. 400π m^2
B. 300πm^2
C. 250πm^2
D. 200πm^2
E. 100πm^2



This question seems incomplete or isn't worded properly. Can someone help
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Re: A circular swimming pool is surrounded by a wall with a height of 2m.  [#permalink]

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New post 22 May 2020, 21:34
1
Can anybody please explain how answer is 400 \(pi\) sq m :roll:
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Re: A circular swimming pool is surrounded by a wall with a height of 2m.  [#permalink]

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New post 23 May 2020, 09:00
SiddharthR wrote:
MathRevolution wrote:
[GMAT math practice question]

A circular swimming pool is surrounded by a wall with a height of 2m. The area of the wall is 21% of the area of the swimming pool. What is the area of the swimming pool?

A. 400π m^2
B. 300πm^2
C. 250πm^2
D. 200πm^2
E. 100πm^2



This question seems incomplete or isn't worded properly. Can someone help


There were mistakes in words. They are fixed now.
The words "wall" and "height" should be fixed with "walk" and "width", respectively.

Sorry about the mistakes.

Happy Studying !!!
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Re: A circular swimming pool is surrounded by a wall with a height of 2m.  [#permalink]

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New post 23 May 2020, 09:13
Let the radius of walk with the swimming pool in between = r+2
Area of whole area ( swimming pool+ walk) = π(r+2)^2

Given: area of walk is 21% of area of swimming pool.

Area of walk = π(r+2)^2 - πr^2
Therefore,
π(r+2)^2 - πr^2 = 21/100(πr^2)
π{(r+2)^2 - r^2}=π{21/100(r^2)}
(r^2+4+4r)- r^2={21/100(r^2)
4+4r=21/100(r^2)
400+400r=21(r^2)
21(r^2)-400r-400=0
21(r^2)-420r+20r-400=0
21r(r-20)+20(r-20)=0
(r-20)(21r+20)=0
R=20 and -20/21(not possible)
R=20

Area of swimming pool is πr^2
π(20)^2 => 400π

Answer is A

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Re: A circular swimming pool is surrounded by a wall with a height of 2m.  [#permalink]

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New post 24 May 2020, 17:14
=>

Assume the radius of the swimming pool is \(r\).

Then the area of the wall is \(2πr·2 = 4πr.\)

Since we have \(4πr = (\frac{21}{100}) πr^2,\) we have \(21r^2 – 400r + 400 = 0\) or \((21r + 20)(r - 20) = 0.\)

Thus, we have \(r = 20.\)

Then, the area of the swimming pool is \(πr^2 = 400π.\)

Therefore, A is the answer.
Answer: A
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Re: A circular swimming pool is surrounded by a wall with a height of 2m.   [#permalink] 24 May 2020, 17:14

A circular swimming pool is surrounded by a wall with a height of 2m.

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