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

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

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Updated on: 22 Oct 2013, 23:32
1
3
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Difficulty:

45% (medium)

Question Stats:

74% (01:22) correct 26% (02:09) wrong based on 74 sessions

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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 ground?

A. 2
B. 3
C. 4
D. 6
E. 9

However what I see is a tank that has 36pi water in it that is half full. So total volume is 72pi. Since the water has height of 2 feet when placed on a circular base, that means the height of the entire cylinder is 4.

72pi/4 = 18pi

pir^2 = 18pi
r^2 = 18
r=3*sqrt(2)

Where am I going wrong here?

OPEN DISCUSSION OF THIS QUESTION IS HERE: a-closed-cylindrical-tank-contains-36pi-cubic-feet-of-water-134500.html

Originally posted by bschoolnewbie2011 on 21 Feb 2012, 19:17.
Last edited by Bunuel on 22 Oct 2013, 23:32, edited 2 times in total.
Edited the typo: should be 4 feet instead of 2 feet.
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Joined: 27 Jan 2012
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Re: Error in Official Guide Diagnostic #5?  [#permalink]

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21 Feb 2012, 20:08
Ahh I see in the solution that the question say 4 for the height of the water instead of 2. So it was a typo.
Math Expert
Joined: 02 Sep 2009
Posts: 52911
Re: Error in Official Guide Diagnostic #5?  [#permalink]

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21 Feb 2012, 21:31
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 ground?
A. 2
B. 3
C. 4
D. 6
E. 9

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 will be half of the diameter, so r.

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

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GMAT Date: 04-23-2012
Re: A closed cylindrical tank contains 36pi cubic feet of water  [#permalink]

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22 Feb 2012, 07:48
bunuel not understood why its half full when lying on level ground and why its height is 3 , radius = 3 even i got but how its height also 3, please explain. thanks
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Joined: 02 Sep 2009
Posts: 52911
Re: A closed cylindrical tank contains 36pi cubic feet of water  [#permalink]

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22 Feb 2012, 08:20
1
pbull78 wrote:
bunuel not understood why its half full when lying on level ground and why its height is 3 , radius = 3 even i got but how its height also 3, please explain. thanks

If some container is half full by volume it'll be half full no matter the position of the container. How else?

Now, if you place the cylinder from the question on a side the diameter of the base of the cylinder becomes height and since cylinder is half full, the level of the water (new height of the water) will equal to r, which is half of the diameter. I think the diagram below might help to understand it better:
Attachment:

Cylinder.PNG [ 14.91 KiB | Viewed 10178 times ]

Hope it's clear.
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GMAT Date: 04-23-2012
Re: A closed cylindrical tank contains 36pi cubic feet of water  [#permalink]

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22 Feb 2012, 08:30
thanks, understood.
Manager
Joined: 11 Jan 2011
Posts: 62
GMAT 1: 680 Q44 V39
GMAT 2: 710 Q48 V40

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03 Apr 2012, 15:23
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 hight, in feet, of the surface of the water above the ground?

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

I answered the problem correctly but I was wondering if it's just a "rule" that if the cylinder was filled half way, that if placed on its side, the water would still reach half the hight (i.e. the height of the radius). Is there a time when this wouldn't hold true?

Thanks,
Rich
Manager
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Posts: 50
Location: United States (WI)
Concentration: Other
Schools: University of Wisconsin (Madison) - Class of 2014
GMAT 1: 680 Q46 V38
GMAT 2: 760 Q48 V46
GPA: 3.66
WE: Marketing (Manufacturing)

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03 Apr 2012, 16:51
Rich, what you're describing will always be true for a closed container of any shape. No matter the orientation, half (1/3, 1/4, etc) full never changes.

Miller Coors would have a big problem on their hands if a full can of beer somehow turned into a 3/4 can of beer upon a change in the can's orientation!
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Joined: 11 Jan 2011
Posts: 62
GMAT 1: 680 Q44 V39
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03 Apr 2012, 19:34
nsspaz151 wrote:
Rich, what you're describing will always be true for a closed container of any shape. No matter the orientation, half (1/3, 1/4, etc) full never changes.

Miller Coors would have a big problem on their hands if a full can of beer somehow turned into a 3/4 can of beer upon a change in the can's orientation!

Let me clarify.

For example, let's take a rectangular prism with:

length = 10
width = 2
depth = 3

If I fill the prism half full (V = 30 units^3) and place it on its face with the smallest sides (2 x 3), the height would be 5 or length/2.

However, if I place the prism flat on the largest side (10 x 3), the height would have to be 1.

I hope that better illustrates the problem that I'm having...
Math Expert
Joined: 02 Sep 2009
Posts: 52911

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03 Apr 2012, 22:43
1
NvrEvrGvUp wrote:
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 hight, in feet, of the surface of the water above the ground?

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

I answered the problem correctly but I was wondering if it's just a "rule" that if the cylinder was filled half way, that if placed on its side, the water would still reach half the hight (i.e. the height of the radius). Is there a time when this wouldn't hold true?

Thanks,
Rich

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Joined: 28 May 2012
Posts: 1
Re: A closed cylindrical tank contains 36pi cubic feet of water  [#permalink]

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28 May 2012, 22:19
Had the container been 1/4th full with water,what would have been the answer?Diameter/4?
Intern
Joined: 29 May 2012
Posts: 2
Re: A closed cylindrical tank contains 36pi cubic feet of water  [#permalink]

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30 May 2012, 12:02
3
EDIT: I just found out it's a print issue/their mistake. In my book (and the one in Google Books) the height given is 2, not 4 (OG Guide, 13th edition). So beware people, if your OG has 2 in the problem, then the solution given is wrong.

Sorry for bumping this (and my first post on this forum) but I also can't see why the answer is 3.

We have 2 scenarios here: vertical tank and horizontal tank.
And we know this:
- Volume of water: 36pi
- Capacity of tank: 2*36pi
- Height of water when tank is vertical: 2
- Height of tank: 2*2
- Height of water when tank is horizontal: r
- Height of tank when tank is horizontal: 2*r

So the formulas are in attachment.

Now can someone explain to me how the hell the radius is 3?

The solutions use this formula: 36pi = pi*r^2 * 4. But this formula must be wrong because if they are calculating for the vertical position then h = 2 and if they are calculating for the horizontal position then they must use half the area of the base in order to multiply with h = 4.
Attachments

Cylinder.PNG [ 54.67 KiB | Viewed 9436 times ]

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

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22 Oct 2013, 15:03
Dear GMAC,

I really hope you don't have typos like this on the actual GMAT... and this is a real retired question?

H
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Joined: 02 Sep 2009
Posts: 52911
Re: A closed cylindrical tank contains 36pi cubic feet of water  [#permalink]

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22 Oct 2013, 23:33
OPEN DISCUSSION OF THIS QUESTION IS HERE: a-closed-cylindrical-tank-contains-36pi-cubic-feet-of-water-134500.html
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Re: A closed cylindrical tank contains 36pi cubic feet of water  [#permalink]

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16 Oct 2018, 16:41
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Re: A closed cylindrical tank contains 36pi cubic feet of water   [#permalink] 16 Oct 2018, 16:41
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