A closed cylindrical tank contains 36pi cubic feet of water and is fil

SOLUTION

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".

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

Look at the diagram below:


Since the tank is half full when placed upright then naturally it'll also be half full when placed on its side, so the level of the water (when placed that way) will be half of the diameter, so \(r\).

Now, given that \(V_{water}=\pi{*r^2}*H_{water}\);

\(36\pi=\pi{r^2}*4\);

\(r=3\).

Answer: B.


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There are a few different relevant heights in the question:

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.

The height of the water in the tank is given to be 4 feet. Since the tank is filled to half its capacity, the height of the cylinder is 8 ft (though we don't need this).

Volume of the water \(= 36*\pi = \pi*r^2*4\)
r = 3

This is all we need to find the required height. Why? We know that the tank is filled to half its capacity. Imgine you have placed it on its side. If it were full of water, the height of the water in this position would be the diameter of the circular base (which is now the height). Since it is half full, the height of the water will come up to the mid point of the circle i.e. its radius. Since radius is 3, the height of water now will be 3 feet.
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Volume of water inside cylinder = 36pi = pi\(r^2\)h

Here water is filled up to a height of 2 feet, so h=2

\(r^2\) = 18

r=3 \(sqrt2\)

There might be a mistake in the given problem.

I agree to your comment partially, in my opinion this question has some ambiguity when it states that the tank contains 36pi cubic feet of water and is filled to half its capacity, so we may assume that 36pi is the volume when half capacity. So it would be better to state that the tank, when full, can be filled with 36pi or the full capacity of the tank is 36pi, or something alike. But i think this is one of the small tricks of GMAT. But anyway if you solved this way and did not come up with answer you should see what else GMAT could think by saying 36pi, then you see that only possible answer is 3 (B)

I wanted to clarify one point. Is there any rule that we refer when we claim that regardless of position of cylinder the water in it will occupy its half?

How else? If water occupies half of the capacity of the tank when it is placed upright, can it occupy other fraction when it is placed on its side???
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how do you know the height is 4 feet when placed on its side?

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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Bunuel

Two questions on the highlight

Q1) Is this the case for EVERY figure --- what about if it were a cube or an empty trapezium for example ?

Q2) Does your assumption not depend on the length and radius or does these factors not count at all -- this rule can be memorized for every geometrical figure

If something is filled to half its capacity, then it's filled to half its capacity no matter how the vessel is placed. How else?
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Hi All,

We’re told that a cylindrical tank (re: a cylinder/tube) contains 36pi cubic feet of water and is filled to HALF of its capacity; when placed upright, the water reaches 4 feet high. We’re asked how high the water reaches when the tank is placed on its side.

One of the ‘keys’ to solving this question quickly is to realize that since the tank is HALF-full, regardless of which side the tank is laying on, the water will reach HALF of the height.

Volume of a cylinder is (pi)(Radius^2)(Height), so we can use that formula – along with what we know about the water – to figure out the radius of the tank…

V = (pi)(R^2)(H) =
36pi = (pi)(R^2)(4)
36 = (R^2)(4)
9 = R^2
R = 3

Thus, the radius of the tank is 3 feet and its diameter is 6 feet. When the cylinder is lying on its side, the water will go to the half-way point of the cylinder. Since the diameter is 6 feet, the half-way point would be the radius: 3 feet.

Final Answer:

GMAT assassins aren't born, they're made,
Rich

JeffTargetTestPrep Magoosh EMPOWERgmatRichC what if it was 1/3rd full? Would the height of the water be 1/3rd of the diameter and pls explain your reason ThatDudeKnows

I think you might have tagged me by accident since I haven't posted on this thread, but here's my take on your question. Look at this diagram. The horizontal lines are 1/3 of the diameter from each other. Are the areas in the bottom section and middle section equal? I don't need to be able to do a geometric proof to show that they aren't! Visual estimation is your friend on GMAT geometry questions.

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