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A closed cylindrical tank contains 36π cubic feet of water

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

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New post 06 Jul 2010, 20:36
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A closed cylindrical tank contains 36π 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

Official Guide 12 Question

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Question: 5
Page: 20
Difficulty: 750

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Last edited by GMATSA on 06 Jul 2010, 21:02, edited 1 time in total.

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Re: Question 5 Manhattan Diagnostic test. [#permalink]

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New post 06 Jul 2010, 21:40
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[quote2GMATSA]I said: 36π = πr²(8) as the tank is half full and the water is 4ft high, the tank must be 8ft .[/quote2]

Hi,

the problem is that you are equating HALF of the cylinder's volume to FULL height. We know that 36pi is half of the cylinder's volume. So, when standing upright, we will have:

V/2 = pi*(r^2)*(h/2)

So, we will have:

36*pi = pi*(r^2)*(8/2)

Another way to think about it is to just visualize "away" the upper half of the cylinder. Then, it is clear that:

36*pi = pi*(r^2)*4

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Re: Question 5 Manhattan Diagnostic test. [#permalink]

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New post 06 Jul 2010, 21:53
Thanks so much, maybe my problem is comprehension.

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Re: Question 5 Manhattan Diagnostic test. [#permalink]

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New post 07 Jul 2010, 00:33
Hi,
Think that a faster way would be to see that the cylinder is half full. Then you need to find the radius of the base since when the cylinder is in horizontal position it will be again half full i.e. to the middle of the base.
4*(r^2)*pi=36*pi, then r=3

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

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New post 26 Dec 2012, 00:08
stuck on this question.
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Re: A closed cylindrical tank contains 36π cubic feet of water [#permalink]

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Re: A closed cylindrical tank contains 36π cubic feet of water   [#permalink] 26 Dec 2012, 03:58
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