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# Water is leaking out from a cylinder container at the rate

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Manager
Joined: 04 Sep 2006
Posts: 112
Water is leaking out from a cylinder container at the rate  [#permalink]

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27 Jun 2009, 21:29
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Difficulty:

35% (medium)

Question Stats:

73% (02:18) correct 27% (02:19) wrong based on 305 sessions

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Water is leaking out from a cylinder container at the rate of 0.31 m^3 per minute. 10 minutes later, the water level decreases 0.25 meter, what is value of the radius?

(A) 0.5
(B) 1.0
(C) 1.5
(D) 2.0
(E) 2.5
Manager
Joined: 27 Jun 2008
Posts: 135

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22 Jul 2009, 00:17
Total water loss = 3.1 mtr in 10 min @.31 meter per min
3.14XR^2X.25 = 3.1
r^2 = 4
r=2

(D)
Intern
Joined: 17 Nov 2009
Posts: 33
Schools: University of Toronto, Mcgill, Queens

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20 Feb 2010, 11:08
irajeevsingh wrote:
Total water loss = 3.1 mtr in 10 min @.31 meter per min
3.14XR^2X.25 = 3.1
r^2 = 4
r=2

(D)

Can you please elaborate that how you did

3.1 * r^2 * .25 = 3.1
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Math Expert
Joined: 02 Sep 2009
Posts: 52296

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20 Feb 2010, 12:00
3
1
Bullet wrote:
irajeevsingh wrote:
Total water loss = 3.1 mtr in 10 min @.31 meter per min
3.14XR^2X.25 = 3.1
r^2 = 4
r=2

(D)

Can you please elaborate that how you did

3.1 * r^2 * .25 = 3.1

In 10 min the volume of the water which leaked out the cylinder would be $$10*0.31=3.1$$ m^3.

Volume = $$\pi*r^2*height=3.1$$ --> $$\pi*r^2*0.25=3.1$$ --> $$\pi=3.14$$ --> $$3.14*r^2*0.25=3.1$$ --> $$r=2$$ (approximately).

Hope it's clear.
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Joined: 17 Nov 2009
Posts: 33
Schools: University of Toronto, Mcgill, Queens

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20 Feb 2010, 22:39
Bunuel wrote:
Bullet wrote:
irajeevsingh wrote:
Total water loss = 3.1 mtr in 10 min @.31 meter per min
3.14XR^2X.25 = 3.1
r^2 = 4
r=2

(D)

Can you please elaborate that how you did

3.1 * r^2 * .25 = 3.1

In 10 min the volume of the water which leaked out the cylinder would be $$10*0.31=3.1$$ m^3.

Volume = $$\pi*r^2*height=3.1$$ --> $$\pi*r^2*0.25=3.1$$ --> $$\pi=3.14$$ --> $$3.14*r^2*0.25=3.1$$ --> $$r=2$$ (approximately).

Hope it's clear.

Thanks Bunuel, I was confusing 3.14 with the volume where is was pi.

Cheers!
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Manager
Joined: 27 Aug 2014
Posts: 138
Concentration: Finance, Strategy
GPA: 3.9
WE: Analyst (Energy and Utilities)
Re: Water is leaking out from a cylinder container at the rate  [#permalink]

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13 Mar 2015, 06:48
Bunuel wrote:
Bullet wrote:
irajeevsingh wrote:
Total water loss = 3.1 mtr in 10 min @.31 meter per min
3.14XR^2X.25 = 3.1
r^2 = 4
r=2

(D)

Can you please elaborate that how you did

3.1 * r^2 * .25 = 3.1

In 10 min the volume of the water which leaked out the cylinder would be $$10*0.31=3.1$$ m^3.

Volume = $$\pi*r^2*height=3.1$$ --> $$\pi*r^2*0.25=3.1$$ --> $$\pi=3.14$$ --> $$3.14*r^2*0.25=3.1$$ --> $$r=2$$ (approximately).

Hope it's clear.

I have a question, that here it is assumed that the cylinder is standing on the radius and the water is being decreased in the length of the cylinder. Is this a good assumption?
I think this should be stated in the question, as I was trying the problem with the cylinder lying on the length.
Math Expert
Joined: 02 Aug 2009
Posts: 7209
Re: Water is leaking out from a cylinder container at the rate  [#permalink]

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13 Mar 2015, 08:04
santorasantu wrote:

I have a question, that here it is assumed that the cylinder is standing on the radius and the water is being decreased in the length of the cylinder. Is this a good assumption?
I think this should be stated in the question, as I was trying the problem with the cylinder lying on the length.

hi,
since the question says the water decreased by .25m , it would mean that the height of it .. since if it is lying as you have taken, this .25m does not have same cross section at any place...
Also you have to take a cylinder as on base because that is what is the original shape..
you can take the way you have taken only when it is specified that way..
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Joined: 27 Nov 2014
Posts: 45
Re: Water is leaking out from a cylinder container at the rate  [#permalink]

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14 Mar 2015, 00:59
chetan2u

hi,
since the question says the water decreased by .25m , it would mean that the height of it .. since if it is lying as you have taken, this .25m does not have same cross section at any place...
Also you have to take a cylinder as on base because that is what is the original shape..
you can take the way you have taken only when it is specified that way..
_____________________________________________________________________________________________________
Chetan i am not convinced from the ans i.e 3.14*$$r^2$$*h
why we took height = .25m as it is not the actual total height ??
and total volume =3.1 as it leaked for 10 min only given.

Regards
SG
Math Expert
Joined: 02 Aug 2009
Posts: 7209
Re: Water is leaking out from a cylinder container at the rate  [#permalink]

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14 Mar 2015, 04:00
1
smartyguy wrote:
.
_____________________________________________________________________________________________________
Chetan i am not convinced from the ans i.e 3.14*$$r^2$$*h
why we took height = .25m as it is not the actual total height ??
and total volume =3.1 as it leaked for 10 min only given.

Regards
SG

hi SG,

Water is leaking out from a cylinder container at the rate of 0.31 m^3 per minute. 10 minutes later, the water level decreases 0.25 meter, what is value of the radius?

(A) 0.5
(B) 1.0
(C) 1.5
(D) 2.0
(E) 2.5

in one minute, the volume of water lost is .31$$m^3$$
so in 10 minutes the volume of water lost is 3.1$$m^3$$..(1)

now, we are also said that the height lost is .25m, we are not concerned with the entire height...
what is the volume of water in this .25m...
since it is a cylinder the volume of .25 m= pi*$$r^2$$*h=3.14*$$r^2$$*.25...
3.14*$$r^2$$*.25=3.1...
$$r^2$$=1/.25=4.. so r=2 approx
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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html

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Intern
Joined: 27 Nov 2014
Posts: 45
Re: Water is leaking out from a cylinder container at the rate  [#permalink]

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14 Mar 2015, 06:27
chetan2u

Hmm it doesn't matter what is the exact total height and volume .

Thanks again chetan

Regards
SG
Intern
Joined: 27 Nov 2014
Posts: 45
Re: Water is leaking out from a cylinder container at the rate  [#permalink]

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14 Mar 2015, 06:28
chetan2u

Hmm it doesn't matter what is the exact total height and volume .

Thanks again chetan

Regards
SG
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Re: Water is leaking out from a cylinder container at the rate  [#permalink]

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18 Jan 2018, 07:51
vcbabu wrote:
Water is leaking out from a cylinder container at the rate of 0.31 m^3 per minute. 10 minutes later, the water level decreases 0.25 meter, what is value of the radius?

(A) 0.5
(B) 1.0
(C) 1.5
(D) 2.0
(E) 2.5

Since the rate of leaking is 0.31 m^3 per minute, in 10 minutes, 10 x 0.31 = 3.1 m^3 of water has been leaked. Let’s let r = radius of the cylinder. Recall that the formula for the volume of a right circular cylinder is V = πr^2h. Using the volume of water leaked and the height associated with that volume, we can create the following equation:

πr^2 x 0.25 = 3.1

πr^2 / 4 = 3.1

r^2 = 3.1 x 4 / π

Notice that π ≈ 3.1, thus we have:

r^2 = 4

r = 2

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Re: Water is leaking out from a cylinder container at the rate &nbs [#permalink] 18 Jan 2018, 07:51
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