13th edition diagnostic exam question #5

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13th edition diagnostic exam question #5

by msbelasco » Fri Jul 27, 2012 10:29 am
Question:
A closed cylindrical tank contains 36(pie) cubic ft of water and is filled to half its capacity. When the tank is placed in its upright position on its circular base on level ground, the height of the water tank is 2 feet. When the tank is placed on its side on level ground, what is the height, in feet, on the surface of the water above the ground?

I need some clarification on this.

I understand the idea is to find the radius of the base, however, in order to find the correct radius you must know what the cylinder's volume is at full capacity correct? I thought the correct way to do this question would be to double what the volume was at half capacity from 36(pie) to 72(pie) for the full volume of the cylinder, as well as double the height of the water from 2 to 4, in order to find the correct measurement of the radius. So, the equation I used was as follows:

72(pie) = (pie)r^2 x 4

Only the official guide claims to just use the volume at half capacity, which was 36(pie), but wouldn't the volume of 36(pie) give you a inaccurate measurement of the radius because this is only half the volume capacity of the cylinder? Please help!

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by KapTeacherEli » Fri Jul 27, 2012 11:14 am
The volume of 36pi has a height of two--in other words, you can divide both sides of your equation by 2 and the result will be the equation in the OG explanation. They're the same thing!
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by msbelasco » Fri Jul 27, 2012 2:34 pm
Thank you for your response!

yes, that is what I thought, but the OG explanation says that the following is the correct formula:

36(pie)= (pie)r^2 x 4

If I'm not mistaken, you are saying the equation will either be

36(pie) = (pie)r^2 x 2

or

72(pie) = (pie)r^2 x 4

The formula they provide, shown above, is what they use, and their conclusion is that the radius is 3. Doing it the way I assumed it should have been done, which i believe is the same way you are claiming, my answer is 3(the square root of)2. Can you please help further? Thanks for your time. [/b]

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by KapTeacherEli » Sat Jul 28, 2012 9:07 am
Let me track down a copy of the OG--I'll get back to you Monday!
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by KapTeacherEli » Fri Aug 03, 2012 12:25 pm
All right--as near as I can tell, this question stem uses somewhat ambiguous language, which is surprising, but apparently official. As near as I can tell, when it says that the cylinder "contains" 36pi cubic feet of water, that means that the capacity is 36pi--not it's currently filled amount. Since it is filled halfway, the current volume of water in the tank is actually 18pi--therefore, 18pi = pi r ^2 * (2) or 36pi = pi r^2 * (4) are, respectively, the formulas to calculate the radius based on the volume of the entire tank and the volume of the actual water.

This was definitely a tough one, though--thanks for your patience while I looked into it!
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by msbelasco » Fri Aug 03, 2012 12:51 pm
Thanks for the response, Eli! Actually,I'm finding many problems with vague wording that have resulted in wrong answers in the OG, which has me really concerned.

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by aanavek » Thu Sep 27, 2012 1:13 pm
This one really was so confusing for me, there sure is difference between "can contain" vs "contains". I don't quite understand how "contains" needs to be interpreted as "max capacity".

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by GMATGuruNY » Thu Sep 27, 2012 7:38 pm
msbelasco wrote:Question:
A closed cylindrical tank contains 36(pie) cubic ft of water and is filled to half its capacity. When the tank is placed in its upright position on its circular base on level ground, the height of the water tank is 2 feet. When the tank is placed on its side on level ground, what is the height, in feet, on the surface of the water above the ground?

I need some clarification on this.

I understand the idea is to find the radius of the base, however, in order to find the correct radius you must know what the cylinder's volume is at full capacity correct? I thought the correct way to do this question would be to double what the volume was at half capacity from 36(pie) to 72(pie) for the full volume of the cylinder, as well as double the height of the water from 2 to 4, in order to find the correct measurement of the radius. So, the equation I used was as follows:

72(pie) = (pie)r^2 x 4

Only the official guide claims to just use the volume at half capacity, which was 36(pie), but wouldn't the volume of 36(pie) give you a inaccurate measurement of the radius because this is only half the volume capacity of the cylinder? Please help!
I suspect that 2 feet is a misprint. in the OG12, the height of the water is given as 4 feet.
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by aceacharya » Sat Mar 09, 2013 11:49 pm
yep the talk on other forums is the same that it is a misprint in the 13th edition of the OG

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by imtheboss » Wed Jun 05, 2013 9:45 pm
THANK YOU for the strong suggestion that this is a misprint! I thought I was going crazy. I also thought that 36pi = half volume of the cylinder.

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by victoryspear » Tue Jan 14, 2014 10:38 am
Hi,

I would suggest that MBA.com publishes this as an errata on the website.
It feels strange to have a vaguely worded question and answers that don't really fit in!

Regards,
Vetrivel