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cylinder question

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by ohjoon2 » Sat Jul 17, 2010 6:38 pm
a question from the official guide for gmat review (12th edition) diagnostic test.

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 the ground?
(A) 2
(B) 3
(C) 4
(D) 6
(E) 9

the answer is B.
according to the answer key, they got this answer by...
V = (pi)(r^2)(h) <----formula for volume of cylinder
36pi = (pi)(r^2)(h) <-----just input the values given
solve for r and that's the answer.

my question is....if the tank was only filled to HALF of its capacity, why didn't the answer key divide the 36pi in half?
shouldn't the thought process be ...
(36pi)/2 = (pi)(r^2)(h)
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by Patrick_GMATFix » Sat Jul 17, 2010 6:53 pm
Hi ohjoon,

[Note this is OG 12 #5 on page 20. The OG Companion's solution is attached. If you cannot see the attachment, read it here]

When the cylinder is upright, the water (which fills half of the original cylinder) is also in the shape of a cylinder. The explanation is correct because the formula is used to find the volume of the water, not the volume of the whole cylinder. Note that in the official explanation, the height used is 4 (the height of the water). Since the water and the entire cylinder have the same base, finding the radius of the cylinder. 36 = pi*r^2*4 works because 36 is the volume of the water and 4 is the height of the water.

The formula you suggested is not correct. It seems you mistook 36 as the volume of the whole cylinder when it is really the volume of the water. The answer is B

Hope that helps,
-Patrick
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by ohjoon2 » Sat Jul 17, 2010 6:59 pm
i get it now.

my confusion was... i knew the volume of the water was 36pi, but the formula for volume of cylinder applies to the entire cylinder. so i wondered why are they using the volume of the entire cylinder and using that to equal the volume of water. but, i did fail to recognize that they provided the height of water, not the whole cylinder. so thanks for pointing that out.
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by Patrick_GMATFix » Sat Jul 17, 2010 7:02 pm
No problem. Edited my post to be more thorough, but I'm glad you got it.
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by outreach » Sun Jul 18, 2010 12:00 am
pi(r^2)4 = 36pi

r^2 = 36pi/4pi = 9

r = 3

When tank is placed on its side, water will occupy half the volume.

=> one side total height will be 2r

But, for half vol the height will be half = 2r/2 = r = 3
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