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Re: A closed cylindrical tank contains 36pi cubic feet of watank [#permalink]

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25 Mar 2014, 08:36

Hi everyone! this is how i answered this question: I took the 36pi to mean 1/2 of the volume so the full volume must be 72pi. the tank is half full standing up and must be half full on its side, the height of the water equals the radius- as previous posters have proven. I have the guide that gives the height of the water as 2 so the height of the tank is 4. We know V= pi*r^2*h and we need to find r

So: 72pi = pi*r^2*4 72/4 = r^2 18 = r^2: r = 3 root 2 which is not one of the answer choices. if there is a typo, having the height of half the tank at 4 gives h=8 which divides nicely into 72 which gives you r^2=9, r=3, answer B.

The answer in the book uses V=36pi which represents the known volume of water (which is half full) not the volume of the tank. Substituting everything in: h=4, v=36pi, r=? 36pi = pi*r^2*4 9=r^2 r=3 so 36pi of water reaches 3 feet (the radius) but if the total volume of the tank is 72pi then the radius is 3root2, which is not 3

Im super confused! Which way is correct??? Can we use the value of the known volume of a liquid to find r?? I thought V has to represent the volume of the container, not necessarily whats inside

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

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05 Apr 2015, 09:38

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

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18 Aug 2015, 12:14

Extending the question - what if water is not half of the capacity or an easy number like 1/2 or 1/4 or 1/8. what is the shape of water when cylinder is placed on its side?

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

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03 May 2016, 09:39

Bunuel wrote:

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

Notice that some editions of OG have a typo saying that the height of the water in the tank is 2 feet, it should read "the height of the water in the tank is 4 feet".

Okay many people are confused about this question. So let's make the stem a bit clearer. We are given 36pi occupies half the volume of the cylinder. Now it does not matter in what orientation we keep the cylinder. half the volume will always occupy half the cylinder. Now when cylinder is upright then half of its height is 4 feet bcz water occupies half the cylinder space. Refer to Bunuel's diagrams. But when we place cylinder horizontal to the ground the diameter of the circle becomes the new height. Now again the water should occupy half the cylinder space. So it should occupy the radius length above the ground. we know 1/2 pi*r^2*h=36 where h =8. So answer is 3. Hope this helps.

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

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10 Jan 2017, 04:35

This is my approach. Regardless of the shift of the cylinder the h (height) and r (radius) , will remain always the same. V= 36π (volume of water when cylinder is filled in half capacity) --> so the max volume of the cylinder is 2 ∗36π =72π

Volume = π∗r^2∗h (The question asks for the radius in a confusing way) Here we have to notice that the new height = radius of cylinder ,so max volume is : 72π=π∗r^2∗8 (since its h= 4 feet when half capacity-->h=8 will be on full capacity) 72=8∗r^2 r^2=72/8 r^2=9 r= 3 answer is B

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

We are given that a closed cylindrical tank that is half full contains 36π cubic feet of water, and the height of the water is 4 feet. We can thus say that the full tank would have 72π cubic feet of water at a height of 8 feet. Using the volume formula, we can now determine the radius of the circular base:

volume = π(r^2)h

72π = π(r^2)(8)

9 = r^2

r = 3 feet

We see that the radius is 3 feet.

We need to determine the height of the water when the tank is placed on its side on level ground. When the cylinder is turned on its side, the diameter now represents the new height, and since the tank is half full, the new height of the water is equivalent to the radius, so the new height of the water is 3 feet.

Answer: B
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