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Geometry - Don't agree with book answer

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Geometry - Don't agree with book answer

by dalia0853 » Sat Jan 05, 2013 1:52 am
The following is a question from the the GMAT Official Review 13th edition. I am not in agreement with the answer provided by the book. Please help explain.

A closed cylindrical tank contains 36Ï€ 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 the ground?

My solution: 36Ï€ = (Ï€r^2xh)/2 ; h being the full hight of the cylinder and r being the radius of the base.

The book's solution: 36π = πr^2xh

If 36Ï€ represents the water volume which represents only half of the volume of the cylinder, how can the book be right?

Can someone please help on this one?

Thanks,


Dalia
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by sana.noor » Sat Jan 05, 2013 3:22 am
since the question says that the water is half filled it means when the tank is placed on its side then still it hold half the water which will be equal to half the diameter(raduis).
36 pie = pie r^2 H
36 pie = pie r^2 4
solving this equation we get r^2 = 9 and r = 3
as r is half the diameter so the height of the water will be 3 feet. what is the official answer?
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by dalia0853 » Sat Jan 05, 2013 3:47 am
The official answer is 3.

However, how can 36π = πr^2x4?
36π is half the volume of the cylinder since the water is only filling half of the cylinder. So It should be 36π = πr^2x2 or 72π = πr^2x4.
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by sana.noor » Sat Jan 05, 2013 4:03 am
the big mistake u r doing is dividing pie r^2 h with 2 or taking full volume of cylinder to 72. here we are not concern about he full volume of the cylinder but we are concerned with the volume of water that is 36.
the question tells that the water is half full in a cylinder whose volume is 36 and height is 4 feet when the circular end is the base. you don't really need this formula. picture the cylinder placed on its side. the height will become the base and the circular side will become the height. now the water is still half full. the total height of the cylinder when placed on its side is equal to the diameter of the cylinder. water is half full that means it covers half the volume of the cylinder whose height is equal to half the diameter. using formula of volume of cylinder
volume of cylinder is = V = pie r^2 h but formula for the volume of the water in the cylinder will be
36 pie = pie R^2 (4) = pie will be divided by pie and we will be left with 36 = r^2 (4). 9 = R^2
Now r = 3. radius is half of the diameter and it will be the height of the water when the cylinder is placed on its side.
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by Param800 » Sat Jan 05, 2013 4:04 am
A closed cylindrical tank contains 36Ï€ 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 the ground?
There is a typo, the bold part should be 4 not 2. But, your basic understanding is right.. we solve it this way--

pie r^2h = 2 ( 36pie ) .. (i)

We know that h is 4 for half the cylinder...so for full cylinder it will be 8

Plug that in expression (i)

pie r^2 ( 8 )= 2 *36 pie

r^2 = 9

thus, r = 3 Hence the answer.

Hope this clarifies your doubt :)
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by dalia0853 » Sat Jan 05, 2013 4:09 am
Thanks Param800! this clarifies my doubt.

Do you have an official reference showing that this is a typo?

Also, thank you sana.noor for taking the time.
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by sana.noor » Sat Jan 05, 2013 4:15 am
Obviously when we take full height of cylinder then we will take volume equals to 72 and full height to 8 feet, but if we are taking volume half of the cylinder then we take 36 pie and height equals to 4. both the cases wont change the answer. we dont have to go into calculations, if water is half full then its height will equals to half of the height when circular side is the base and half of its diameter when cylinder is placed on its side.
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by Param800 » Sat Jan 05, 2013 4:18 am
You'r Welcome.

Yes,in OG 13 on Pg20. Q.5. It shows the right question
daliajaffal wrote:Thanks Param800! this clarifies my doubt.

Do you have an official reference showing that this is a typo?

Also, thank you sana.noor for taking the time.
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by dalia0853 » Sat Jan 05, 2013 4:45 am
My book says "2 feet" on page 20. Weird.

Hope their are no typos on the real test.

Thanks again!
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by Param800 » Sat Jan 05, 2013 4:56 am
Ya I hope so too !!
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by sana.noor » Sat Jan 05, 2013 5:10 am
my book also says "2 feet" and thus the total height will be 4
formula of volume of cylinder is
V = Pie r^2 (h) using this formula volume is 36 and h is 4 putting these values
36 = pie r^2 (4)
36 = r^2 4
9 = r^2
3 = r
the 3 is the answer. though the answer is coming right but i still feel their is some issue in the question.
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by Param800 » Mon Jan 07, 2013 3:46 am
I found this document which explains why you have a typo in ur book but I don't.

https://media.wiley.com/product_ancillar ... Errata.pdf
daliajaffal wrote:Thanks Param800! this clarifies my doubt.

Do you have an official reference showing that this is a typo?

Also, thank you sana.noor for taking the time.
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