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There are 2 circular cylinders X and Y, and both cylinders contain wat

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There are 2 circular cylinders X and Y, and both cylinders contain wat [#permalink]

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New post 23 Feb 2017, 19:34
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Question Stats:

62% (02:47) correct 38% (01:07) wrong based on 42 sessions

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There are 2 circular cylinders X and Y, and both cylinders contain water inside. Cylinder X has \(5π\) square inches as the base area and 6 inches as the height of the water inside, and cylinder Y has \(10π\) square inches as the base area and 2 inches as the height of the water inside. If the height of the water becomes the same when the water drawn from cylinder X is poured into cylinder Y, what is the height of water in these cylinders, in inches?

A. 2.5   
  
B. 3   
  
C. \(\frac{10}{3}\)   
  
D. 4   
  
E. 4.5
[Reveal] Spoiler: OA

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Re: There are 2 circular cylinders X and Y, and both cylinders contain wat [#permalink]

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New post 23 Feb 2017, 20:24
I did get the solution by brute force. It took me almost 3.5 minutes.
Is there any particular method to solve this.

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There are 2 circular cylinders X and Y, and both cylinders contain wat [#permalink]

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New post 24 Feb 2017, 00:39
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AustinKL wrote:
There are 2 circular cylinders X and Y, and both cylinders contain water inside. Cylinder X has \(5π\) square inches as the base area and 6 inches as the height of the water inside, and cylinder Y has \(10π\) square inches as the base area and 2 inches as the height of the water inside. If the height of the water becomes the same when the water drawn from cylinder X is poured into cylinder Y, what is the height of water in these cylinders, in inches?

A. 2.5   
  
B. 3   
  
C. \(\frac{10}{3}\)   
  
D. 4   
  
E. 4.5


total volume of water in both cylinders X and Y = 5pi*6 + 10pi*2 = 30pi + 20pi = 50pi

when the water drawn from cylinder X is poured into cylinder Y, the height of water becomes same in both X and Y, let the height be H

Therefore, we have
5pi*H + 10pi*H = 50pi (Since total volume will remain same)
15H = 50
H = 10/3

deepthit : hope this helps. :)

Hence option C is correct
Hit Kudos if you liked it 8-)

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Re: There are 2 circular cylinders X and Y, and both cylinders contain wat [#permalink]

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New post 27 Feb 2017, 11:07
AustinKL wrote:
There are 2 circular cylinders X and Y, and both cylinders contain water inside. Cylinder X has \(5π\) square inches as the base area and 6 inches as the height of the water inside, and cylinder Y has \(10π\) square inches as the base area and 2 inches as the height of the water inside. If the height of the water becomes the same when the water drawn from cylinder X is poured into cylinder Y, what is the height of water in these cylinders, in inches?

A. 2.5   
  
B. 3   
  
C. \(\frac{10}{3}\)   
  
D. 4   
  
E. 4.5


First let’s determine the volume of water in each of the two cylinders before water from one is poured into the other. Recall that the volume of a cylinder is V = Bh, in which B is the circular base area and h is the height of the cylinder. Thus we have:

Water in cylinder X: Volume = 5? x 6 = 30? in^3

Water in cylinder Y: Volume = 10? x 2 = 20? in^3

Now we can let w be the amount of water that should be poured from cylinder X to cylinder Y so that the water in both cylinders will be the same height. Notice that if V = Bh, then h = V/B.

Thus we have:

(30? - w)/5? = (20? + w)/10?

5?(20? + w) = 10?(30? - w)

100?^2 + 5w? = 300?^2 - 10w?

15w? = 200?^2

3w = 40?

w = 40?/3

Since w = 40?/3, the height of water in each cylinder is:

(30? - 40?/3)/5?

(90? - 40?)/15?

50?/15? = 10/3

Answer: C
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Re: There are 2 circular cylinders X and Y, and both cylinders contain wat [#permalink]

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New post 10 Nov 2017, 09:40
I really like 0akshay0's method of doing this as it's fairly quick and mathematical. I did it slightly different to get a good quick estimate.

First look at the current volume:
X = 6*5*pi = 30pi
Y = 2*10*pi = 20pi

I then wondered what would happen if you move 10pi of volume from X to Y. The height on x moves down to 4 and the height on Y moves up to 3. Since they are not equal yet, you have to move some more water to where the height will be somewhere between 3 and 4. Since there is only one answer between 3 and 4, I didn't have to move into further calculations.

Just thought I'd share an alternative method. Took a little over a min with most of the time thinking how I wanted to approach it.

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Re: There are 2 circular cylinders X and Y, and both cylinders contain wat   [#permalink] 10 Nov 2017, 09:40
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