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Math Expert V
Joined: 02 Sep 2009
Posts: 59674
A closed cylindrical tank contains 36pi cubic feet of water  [#permalink]

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86 00:00

Difficulty:   55% (hard)

Question Stats: 67% (02:13) correct 33% (02:32) wrong based on 2304 sessions

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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".

Diagnostic Test
Question: 5
Page: 20
Difficulty: 650

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Math Expert V
Joined: 02 Sep 2009
Posts: 59674
Re: A closed cylindrical tank contains 36pi cubic feet of water  [#permalink]

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23
23
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 $$V_{water}=\pi{*r^2}*H_{water}$$ --> $$36\pi=\pi{r^2}*4$$ --> $$r=3$$.

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

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2
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.
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Re: A closed cylindrical tank contains 36pi cubic feet of water  [#permalink]

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2
1
gnan wrote:
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)
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Re: A closed cylindrical tank contains 36pi cubic feet of water  [#permalink]

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1
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?
Math Expert V
Joined: 02 Sep 2009
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Re: A closed cylindrical tank contains 36pi cubic feet of water  [#permalink]

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

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how do you know the height is 4 feet when placed on its side?
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Re: A closed cylindrical tank contains 36pi cubic feet of water  [#permalink]

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Mackam1234 wrote:
how do you know the height is 4 feet when placed on its side?

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

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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

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.

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GMAT 1: 620 Q46 V30 Re: A closed cylindrical tank contains 36pi cubic feet of water  [#permalink]

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1
Volume of cylinder = pi*r^2*h = pi * r^2 * 4 ft = 36 pi
r^2= 9 pi
r=3ft
A cyl which is half full, placed on its side will also be filled up to half its height which is r.

Therefore, r = 3ft.
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Re: A closed cylindrical tank contains 36pi cubic feet of water  [#permalink]

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When the cylinder is placed on its side how is the base circular? Maybe a diagram would have helped.
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Re: A closed cylindrical tank contains 36pi cubic feet of water  [#permalink]

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1/2 volume = 36 pi ft^ 3 when the height of water = 4

Thus max height = 8 and max volume = 72pi ft ^3
Notice if you flip the right cylinder on its side and the cylinder is filled 1/2 way then the water will actually share the height of the radius, so we are looking for the radius.

72pi = pi*r^2*8
r^2=9
r=3
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Re: A closed cylindrical tank contains 36pi cubic feet of water  [#permalink]

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Bunuel wrote:
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 $$V_{water}=\pi{*r^2}*H_{water}$$ --> $$36\pi=\pi{r^2}*4$$ --> $$r=3$$.

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
Math Expert V
Joined: 02 Sep 2009
Posts: 59674
Re: A closed cylindrical tank contains 36pi cubic feet of water  [#permalink]

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jabhatta@umail.iu.edu wrote:
Bunuel wrote:
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 $$V_{water}=\pi{*r^2}*H_{water}$$ --> $$36\pi=\pi{r^2}*4$$ --> $$r=3$$.

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?
_________________ Re: A closed cylindrical tank contains 36pi cubic feet of water   [#permalink] 16 Oct 2019, 20:41
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