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Confused or going crazy - Cylinder Tank

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Confused or going crazy - Cylinder Tank

by quiimari » Sun May 06, 2012 5:51 pm
This is question 5 on the just published 2012 OG and either they made a mistake or I'm going crazy...

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 2 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?

So if half the volume = 36pi, then the cylinder's total volume = 72pi

And if half the height of the tank = 2, then the total height of tank = 4

Solving for the radius, 72pi = r^2(pi)(4)

18 = r^2
r = sqrt(18)

Book says the answer is 3. Only way that works is if the total height of the tank is 8. Did the snobby test makers make an error or have I lost my mind?
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by Anurag@Gurome » Sun May 06, 2012 6:05 pm
quiimari wrote:This is question 5 on the just published 2012 OG and either they made a mistake or I'm going crazy...

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 2 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?

So if half the volume = 36pi, then the cylinder's total volume = 72pi

And if half the height of the tank = 2, then the total height of tank = 4

Solving for the radius, 72pi = r^2(pi)(4)

18 = r^2
r = sqrt(18)

Book says the answer is 3. Only way that works is if the total height of the tank is 8. Did the snobby test makers make an error or have I lost my mind?
The questions is: 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

It is given that the tank is half full when placed upright, which means it will be half full when placed on its side. So, the level of water will be half of the diameter, which means it will be r.

Volume of cylinder = (pi)r²h
36(pi) = (pi)r² * 4 ft
r² = 9
r = 3 ft

The correct answer is B.
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by quiimari » Sun May 06, 2012 9:46 pm
Anurag@Gurome wrote:
quiimari wrote:This is question 5 on the just published 2012 OG and either they made a mistake or I'm going crazy...

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 2 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?

So if half the volume = 36pi, then the cylinder's total volume = 72pi

And if half the height of the tank = 2, then the total height of tank = 4

Solving for the radius, 72pi = r^2(pi)(4)

18 = r^2
r = sqrt(18)

Book says the answer is 3. Only way that works is if the total height of the tank is 8. Did the snobby test makers make an error or have I lost my mind?
The questions is: 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

It is given that the tank is half full when placed upright, which means it will be half full when placed on its side. So, the level of water will be half of the diameter, which means it will be r.

Volume of cylinder = (pi)r²h
36(pi) = (pi)r² * 4 ft
r² = 9
r = 3 ft

The correct answer is B.
So they did make a mistake. The book says 2 feet

https://books.google.com/books?id=sQW_fK ... de&f=false
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by Bill@VeritasPrep » Mon May 07, 2012 7:31 am
Yes, they did. I had the same reaction you did when I did that problem; I just could not figure out what I did wrong!
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by amelia.narine » Tue May 22, 2012 7:59 pm
I had the same problem too..where i went wrong is reading the question and interpreting it incorrectly..the question states: A closed cylindrical tank contains 36 cubic feet of water this means that the tank can only contain 36 cubic feet of water.

So using the area of a cylinder formula and calculating for r using 36 as the total volume will result to 3.
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by benjiboo » Sun Sep 02, 2012 10:58 am
I dont know if I agree that it is not a mistake...

"A closed cylindrical tank contains 36(pie) cubic ft of water and is filled to half its capacity."...

First off, if its "closed" then we are to assume there is no way to open it, therefore, whatever is in it... is in it. And nothing is coming out.

The word 'and' is offering additional information - in the present, not in the past or future. It doesnt say "and THEN"...

If this is not a mistake, then the wording is so ambiguous that I could go around saying, "My closed sealed box of Captain Crunch cereal contains 300 pieces of cereal and is empty" You'd really sit there wondering if I was on drugs... how could it contain 300 pieces AND be empty? Someone clarify?
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by Ian Stewart » Sun Sep 02, 2012 9:53 pm
The strange thing is, in OG12, the question is right - it says that the height of the water is 4 feet (which is probably why Anurag said that the question reads that way; it used to). But in OG13 they changed just that one number in the question to '2', and now the question is simply wrong. So yes, it's a typo, and no, I have no idea why they ruined a perfectly good question in the newer edition of the book.
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by vk_vinayak » Mon Sep 03, 2012 6:53 am
I own a hardcopy of OG 13(Indian sub-continent edition) and the question is printed correctly in it.
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by kelleygrad05 » Sun Dec 02, 2012 11:59 pm
Thank GOD you guys took a few minutes to clarify. Never feel quite right moving on without reconciling a mistake I made. Seriously, thank you.
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by Resp007 » Mon Sep 02, 2013 7:31 am
okay so I had a bad test and thought let me reset and re-do everything. I was scratching my head why I cant understand a question like this that doesn't require a pen to solve. So well solved it 5-6 times assuming I may be doing something wrong or silly mistake somewhere and then finally referred to solution and wow, it destroyed my confidence. Then I came here and... what the hell man. I need a break perhaps.
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