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A closed cylindrical tank contains 36pi cubic feet of water [#permalink]

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14 Jun 2012, 02:54

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A closed cylindrical tank contains 36pi cubic feet of water and is filled to half its capacity. When the tank is placed upright on its circular base on level ground, the height of the water in the tank is 4 feet. When the tank is placed on its side on level ground, what is the height, in feet, of the surface of the water above the ground?

(A) 2 (B) 3 (C) 4 (D) 6 (E) 9

Notice that some editions of OG have a typo saying that the height of the water in the tank is 2 feet, it should read "the height of the water in the tank is 4 feet".

Diagnostic Test Question: 5 Page: 20 Difficulty: 650

Re: A closed cylindrical tank contains 36pi cubic feet of water [#permalink]

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14 Jun 2012, 02:54

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SOLUTION

Notice that some editions of OG have a typo saying that the height of the water in the tank is 2 feet, it should read "the height of the water in the tank is 4 feet".

A closed cylindrical tank contains 36pi cubic feet of water and is filled to half its capacity. When the tank is placed upright on its circular base on level ground, the height of the water in the tank is 4 feet. When the tank is placed on its side on level ground, what is the height, in feet, of the surface of the water above the ground?

(A) 2 (B) 3 (C) 4 (D) 6 (E) 9

Look at the diagram below:

Since the tank is half full when placed upright then naturally it'll also be half full when placed on its side, so the level of the water (when placed that way) will be half of the diameter, so \(r\).

Now, given that \(V_{water}=\pi{*r^2}*H_{water}\) --> \(36\pi=\pi{r^2}*4\) --> \(r=3\).

Re: A closed cylindrical tank contains 36pi cubic feet of water [#permalink]

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14 Jun 2012, 10:43

Bunuel, I think there is some error in the question as none of the answer choices are correct.

Here is my approach:

Volume of water = π(r^2)h = 2π(r^2) = 36π - As height of water is 2 feet => r^2 = 18 => r = sqrt(18)

As the tank is regular shaped, the water level will be half of its height irrespective of the position of the cylinder. So when its lying flat, height of water will be half of diameter = radius = r = sqrt(18)

None of the answer choices has this, so it should either be sqrt(36) or sqrt (9) - I think the problem might have a problem!

Re: A closed cylindrical tank contains 36pi cubic feet of water [#permalink]

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16 Jun 2012, 03:56

gnan wrote:

Volume of water inside cylinder = 36pi = pi\(r^2\)h

Here water is filled up to a height of 2 feet, so h=2

\(r^2\) = 18

r=3 \(sqrt2\)

There might be a mistake in the given problem.

I agree to your comment partially, in my opinion this question has some ambiguity when it states that the tank contains 36pi cubic feet of water and is filled to half its capacity, so we may assume that 36pi is the volume when half capacity. So it would be better to state that the tank, when full, can be filled with 36pi or the full capacity of the tank is 36pi, or something alike. But i think this is one of the small tricks of GMAT. But anyway if you solved this way and did not come up with answer you should see what else GMAT could think by saying 36pi, then you see that only possible answer is 3 (B) _________________

If you found my post useful and/or interesting - you are welcome to give kudos!

Re: A closed cylindrical tank contains 36pi cubic feet of water [#permalink]

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16 Jun 2012, 04:13

Tricky. 650+ level.

Volume of the Cylinder: pi*r^2*h= 36pi

r^2*2=36 r^2=18 r=Sq root 18

Something wrong with the answer choices. This question is similar to one in OG12 except the height given is 4 feet there. Answer choices given are same.

Re: A closed cylindrical tank contains 36pi cubic feet of water [#permalink]

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22 Jun 2012, 03:02

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SOLUTION

Notice that some editions of OG have a typo saying that the height of the water in the tank is 2 feet, it should read "the height of the water in the tank is 4 feet".

A closed cylindrical tank contains 36pi cubic feet of water and is filled to half its capacity. When the tank is placed upright on its circular base on level ground, the height of the water in the tank is 4 feet. When the tank is placed on its side on level ground, what is the height, in feet, of the surface of the water above the ground?

(A) 2 (B) 3 (C) 4 (D) 6 (E) 9

Look at the diagram below:

Attachment:

Cylinder.PNG [ 14.91 KiB | Viewed 25798 times ]

Since the tank is half full when placed upright then naturally it'll also be half full when placed on its side, so the level of the water (when placed that way) will be half of the diameter, so \(r\).

Now, given that \(V_{water}=\pi{*r^2}*H_{water}\) --> \(36\pi=\pi{r^2}*4\) --> \(r=3\).

Re: A closed cylindrical tank contains 36pi cubic feet of water [#permalink]

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28 Oct 2012, 00:29

p.s. for anyone still coming across this question and confused... If you're getting 3*sqrt(2) as the answer, you're reading a version of the book with the error mentioned in original post.

Re: A closed cylindrical tank contains 36pi cubic feet of water [#permalink]

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22 Oct 2013, 09:34

I wanted to clarify one point. Is there any rule that we refer when we claim that regardless of position of cylinder the water in it will occupy its half? _________________

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Re: A closed cylindrical tank contains 36pi cubic feet of water [#permalink]

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22 Oct 2013, 09:46

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Ergenekon wrote:

I wanted to clarify one point. Is there any rule that we refer when we claim that regardless of position of cylinder the water in it will occupy its half?

How else? If water occupies half of the capacity of the tank when it is placed upright, can it occupy other fraction when it is placed on its side??? _________________

Re: A closed cylindrical tank contains 36pi cubic feet of water [#permalink]

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14 Nov 2013, 19:22

Buneul, I think that surface area water covers when a cylinder is placed on its circular base is NOT EQUAL to the surface area which it covers when placed on the ground along its height. So, height of water from ground will be different in each of the two cases. I agree that volume is the same but because of change in dimensions the height will different in both cases.

Re: A closed cylindrical tank contains 36pi cubic feet of water [#permalink]

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15 Nov 2013, 01:37

Expert's post

madn800 wrote:

Buneul, I think that surface area water covers when a cylinder is placed on its circular base is NOT EQUAL to the surface area which it covers when placed on the ground along its height. So, height of water from ground will be different in each of the two cases. I agree that volume is the same but because of change in dimensions the height will different in both cases.

The question and the solution talk about the volume not surface area. _________________

Re: A closed cylindrical tank contains 36pi cubic feet of water [#permalink]

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17 Nov 2013, 04:58

Bunuel, I understand your solution, however I am not able to understand the problem with my method, (pi*r^2*4)=36*pi r=3 Now since half filled is 36*pi, complete capacity is 72*pi Therefore, pi*3^2*h=72*pi h=8 (i.e height of tank is 8)

Now since tank is placed on it's side, the base is infact the height when the tank is placed upright. So new base = 8, i.e new radius=4 Now pi*4^2*h=36*pi (since 36*pi is the volume of water) From this I get the height of water as, 36/16 Not sure where I am going wrong.

Re: A closed cylindrical tank contains 36pi cubic feet of water [#permalink]

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17 Nov 2013, 12:19

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geetchandratre wrote:

Bunuel, I understand your solution, however I am not able to understand the problem with my method, (pi*r^2*4)=36*pi r=3 Now since half filled is 36*pi, complete capacity is 72*pi Therefore, pi*3^2*h=72*pi h=8 (i.e height of tank is 8)

Now since tank is placed on it's side, the base is infact the height when the tank is placed upright. So new base = 8, i.e new radius=4 Now pi*4^2*h=36*pi (since 36*pi is the volume of water) From this I get the height of water as, 36/16 Not sure where I am going wrong.

The red part doe not make sense. The radius of which circle is 4? _________________

Re: A closed cylindrical tank contains 36pi cubic feet of water [#permalink]

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17 Nov 2013, 21:14

Bunuel wrote:

geetchandratre wrote:

Bunuel, I understand your solution, however I am not able to understand the problem with my method, (pi*r^2*4)=36*pi r=3 Now since half filled is 36*pi, complete capacity is 72*pi Therefore, pi*3^2*h=72*pi h=8 (i.e height of tank is 8)

Now since tank is placed on it's side, the base is infact the height when the tank is placed upright. So new base = 8, i.e new radius=4 Now pi*4^2*h=36*pi (since 36*pi is the volume of water) From this I get the height of water as, 36/16 Not sure where I am going wrong.

The red part doe not make sense. The radius of which circle is 4?

I was wrongly assuming the new base having the new radius. I get it now.

Also, since in this example, we knew that the water is filled to half the tank's capacity, thus when tilted, the water will still occupy half the tank, and we can find the height.

How would you solve it if the water is filled, let's say to 2/3rd the cylinders capacity?

Re: A closed cylindrical tank contains 36pi cubic feet of water [#permalink]

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10 Feb 2014, 21:29

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Mackam1234 wrote:

how do you know the height is 4 feet when placed on its side?

There are a few different relevant heights in the question:

A closed cylindrical tank contains 36pi cubic feet of water and is filled to half its capacity. when the tank is placed upright on its circular base on level ground, the height of the water in the tank is 4 feet.

The height of the water in the tank is given to be 4 feet. Since the tank is filled to half its capacity, the height of the cylinder is 8 ft (though we don't need this).

Volume of the water \(= 36*\pi = \pi*r^2*4\) r = 3

This is all we need to find the required height. Why? We know that the tank is filled to half its capacity. Imgine you have placed it on its side. If it were full of water, the height of the water in this position would be the diameter of the circular base (which is now the height). Since it is half full, the height of the water will come up to the mid point of the circle i.e. its radius. Since radius is 3, the height of water now will be 3 feet. _________________

Re: A closed cylindrical tank contains 36pi cubic feet of water [#permalink]

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08 Mar 2014, 16:53

VeritasPrepKarishma wrote:

Mackam1234 wrote:

how do you know the height is 4 feet when placed on its side?

There are a few different relevant heights in the question:

A closed cylindrical tank contains 36pi cubic feet of water and is filled to half its capacity. when the tank is placed upright on its circular base on level ground, the height of the water in the tank is 4 feet.

The height of the water in the tank is given to be 4 feet. Since the tank is filled to half its capacity, the height of the cylinder is 8 ft (though we don't need this).

Volume of the water \(= 36*\pi = \pi*r^2*4\) r = 3

This is all we need to find the required height. Why? We know that the tank is filled to half its capacity. Imgine you have placed it on its side. If it were full of water, the height of the water in this position would be the diameter of the circular base (which is now the height). Since it is half full, the height of the water will come up to the mid point of the circle i.e. its radius. Since radius is 3, the height of water now will be 3 feet.

Hello Karishma,

This is my first post at GMATClub. I love your Quarter wit, Quarter Wisdom posts also. Anyways, I have a question about this problem. I understand your point about height of the water would be the diameter of the circular base - common sense on first glance. But my thinking is that when you put the cylinder tank on its side, water will occupy the whole height (i.e. 4*2 = 8 feet, see attached picture). The volume is still 36*pi. So now it is pi*r^2*(2h) = 36*pi. In order to keep everything same proportional we should have pi*((3/sqrt(2))^2*2h = 36*pi.

I never question the answer choices provided by Official Guide. Since they had a typo on this question in some editions of Official Guide, I am not so sure about this one.

Thank you so much for helping me understand/dissect this question.

Cheers,

P.S. I have some cylinder style container at work, I will also try it out with a real world precious sample (i.e. h2o) and measure.

EDITED: I understand my mistake now. I missed what Karishma said above -

If it were full of water, the height of the water in this position would be the diameter of the circular base (which is now the height). Since it is half full, the height of the water will come up to the mid point of the circle i.e. its radius. Since radius is 3, the height of water now will be 3 feet.

Attachments

File comment: Source: Modified from Bunuel post

Cylinder.JPG [ 29.47 KiB | Viewed 16050 times ]

Glass_graduated_cylinder-250ml_1.jpg [ 2.23 MiB | Viewed 16180 times ]

Last edited by khanym on 16 Apr 2014, 05:43, edited 1 time in total.

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