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A tank is filled with gasoline to a depth of exactly 2 feet. The tank  [#permalink]

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ENGRTOMBA2018 wrote:
reto wrote:
iamschnaider wrote:
A tank is filled with gasoline to a depth of exactly 2 feet. The tank is a cylinder resting horizontally on its side, with its circular ends oriented vertically. The inside of the tank is exactly 6 feet long. What is the volume of gasoline in the tank?

(1) The inside of the tank is exactly 4 feet in diameter.

(2) The top surface of the gasoline forms a rectangle that has an area of 24 square feet.

From OG 2016 (question 86 DS)

I get why 1 works, but the main qualm I have about 2 is how we can be sure that the 4 feet resulting from the square is a diameter of the circle ie. how we know that it fills the tank exactly up to halfway.

Could someone draw this for Statement 2? I don't get it... reto, see the attached picture.

The trick with statement 2 is that H = 0 when you calculate the value of H from the 2 equations:

$$H^2 + 2^2 = R^2$$

and

R = 2+H , you get H =0

This means that the depth of the gasoline in the cylinder = radius of the cylinder.

Thus, it is sufficient to answer the question.

FYI, we need to know about the radius as without the depth of gasoline = radius of the cylinder, it will be difficult to calculate the volume of the gasoline in the tank.

Hope this helps.

Hi Bunuel VeritasPrepKarishma

My way of thinking is if liquid level is below the centre of the circle then the H= (r-2) ;(Radius from the centre of the circle less 2 feet ) then the equation becomes
(r-2)^2 +2^2 = r^2

and if the liquid is filled till above the centre of the circle then H=(2-r), equation becomes
(2-r)^2+2^2 = r^2.

Though using either of the equation i am getting r=2

Plz correct if i am going wrong somewhere with my understanding. Thanks
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Re: A tank is filled with gasoline to a depth of exactly 2 feet. The tank  [#permalink]

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cruiseav wrote:
Hi Bunuel VeritasPrepKarishma

My way of thinking is if liquid level is below the centre of the circle then the H= (r-2) ;(Radius from the centre of the circle less 2 feet ) then the equation becomes
(r-2)^2 +2^2 = r^2

and if the liquid is filled till above the centre of the circle then H=(2-r), equation becomes
(2-r)^2+2^2 = r^2.

Though using either of the equation i am getting r=2

Plz correct if i am going wrong somewhere with my understanding. Thanks

Yes, your logic is correct. Though, as I mentioned in my solution, this calculation is not required.
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Karishma
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Re: A tank is filled with gasoline to a depth of exactly 2 feet. The tank  [#permalink]

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I'm not sure if this is the correct place to ask, but if the depth was let's say 3ft instead of 2. Would statement 2 still be sufficient?
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Re: A tank is filled with gasoline to a depth of exactly 2 feet. The tank  [#permalink]

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1
ahawkins wrote:
I'm not sure if this is the correct place to ask, but if the depth was let's say 3ft instead of 2. Would statement 2 still be sufficient?

Yes, it would be sufficient. 3 points uniquely define a circle i.e. you can make only one circle with given 3 distinct points. It is the circumcircle of the triangle drawn by connecting the 3 points.
So no matter what the dimensions given to you, the dimensions are uniquely defined.
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Re: A tank is filled with gasoline to a depth of exactly 2 feet. The tank  [#permalink]

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As mentioned in the question stem, the cylinder is lying horizontally and depth or height of the is 2 ft( in horizontal position) , actual height of the cylinder is 6 ft.
so, volume of the tank is 3.14* R^2* 6

S1) diameter is 4ft .
so, R= 2ft and as mentioned depth or height of the is 2 ft( in horizontal position) so volume of the fluid can be derived from here. so its sufficient.

S2) upper surface of fluid forms a rectangle of area 24.
as , h = 6 so A*6= 24, A= 4;
A/2 =2 which is depth or height of the is 2 ft( in horizontal position) so volume of the fluid can be derived from here. so its sufficient.

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Re: A tank is filled with gasoline to a depth of exactly 2 feet. The tank  [#permalink]

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Let´s suppose the water filet is on the center of the cylinder.
Than the water´s height (2 feet) would be the radius of the supposed cylinder, consequently the diameter would be be 4 feet.
Which by the way is the only possible value for water filet´s width.
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A tank is filled with gasoline to a depth of exactly 2 feet. The tank  [#permalink]

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chetan2u wrote:
iamschnaider wrote:
A tank is filled with gasoline to a depth of exactly 2 feet. The tank is a cylinder resting horizontally on its side, with its circular ends oriented vertically. The inside of the tank is exactly 6 feet long. What is the volume of gasoline in the tank?

1) The inside of the tank is exactly 4 feet in diameter.

2) The top surface of the gasoline forms a rectangle that has an area of 24 square feet.

From OG 2016 (question 86 DS)

I get why 1 works, but the main qualm I have about 2 is how we can be sure that the 4 feet resulting from the square is a diameter of the circle ie. how we know that it fills the tank exactly up to halfway.

Hi,
i agree with you however we still can find the answer ..
we can find the chord/diameter of the circular end as 4..
now we have depth as 2, length as 6 and width as 4 but the volume will vary depending on what the dia would be..
there could be two scenarios..
1) where the center is below the chord... that is greater than 2$$\sqrt{3}$$..
eq becomes $$2^2+(2\sqrt{3}+r)^2=r^2$$
r comes out negative so not possible.
2) where the center is above the chord... that is greater than 2$$\sqrt{3}$$.. r can be found so suff..
eq becomes $$2^2+(2\sqrt{3}-r)^2=r^2$$

.

Hi chetan2u

Though i understood the logic i am confused at the first place as how u got 2√3 in the beginning..

Seems like a silly doubt but i am not able to catch it

Thanks..
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Re: A tank is filled with gasoline to a depth of exactly 2 feet. The tank  [#permalink]

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chetan2u wrote:
nycsfmba wrote:
For statement 1 why does the OG Answer Explanation assume that the volume of the gasoline is half the volume of the cylinder? I would have thought the volume of the gasoline is 8π, not 12π. Thanks in advance for your thoughts on what I'm missing.

Hi,
the Q stem tells us the folloeinf info..
A tank is filled with gasoline to a depth of exactly 2 feet...
the statement one tells us that the dia is 4 feet..

so when you join the two information, we can say that the cylinder is half filled

How did we interpret the fact that depth =2 into dia =4 ? Do you also mind elaborating a bit more on statement 2 ?

Thanks a lot !
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Re: A tank is filled with gasoline to a depth of exactly 2 feet. The tank  [#permalink]

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could you please give a clearer and easier approach to this problem? Thanks It is a DS question so some imagination can give us the answer without solving at all. This is what the cylinder looks like:

The question stem tells us that Height = 2 and Length = 6.

Stmnt 1: Diameter = 4

This means the tank is half full. We can find the total volume of the tank using the formula of volume of a cylinder and divide it by 2. We will get the volume of gasoline. Sufficient alone.

Stmnt 2: The area of the rectangle is 24.
We know that the Length is 6 so the other side of the rectangle (as visible in the pic) would be 4. Now imagine this: I have a horizontal line of length 4. If I draw a line from its centre of length 2, I will get a defined arc (which we see is a semi circle but that is irrelevant anyway since it is a DS question).

If there is only one way in which we can make the arc, it means it has defined dimensions and hence the area of this segment can be calculated. Hence the volume of gasoline will be area of this segment * Length of the cylinder.
Sufficient alone.

Hey Karishma,

Thanks for the explanation. However, I do have one doubt related to your explanation for statement 2. Even if we are to calculate the area of the segment, we would still need the angle the segment makes at the center, right? Right now with the current information, we don't have that.
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A tank is filled with gasoline to a depth of exactly 2 feet. The tank  [#permalink]

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Is this an OG question? Why is it so poorly written?!?!

Honestly, I did not really get the meaning of statement 2 until I saw the sketch of one of the experts

"The top surface of the gasoline" - I initially assumed "The top surface of the gasoline's (tank)...", so that the cylinder stands on a rectangular platform.

How can a liquid form a surface equal to a rectangle. I don't want to sound too overly correct but especially for non-natives this wording is very poorly.. would have love to calculate that on my own but I just did not get the meaning.
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Re: A tank is filled with gasoline to a depth of exactly 2 feet. The tank  [#permalink]

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Why do we need either of the statements? Volume=πr2h
R= 3
H= 2

iamschnaider wrote:
A tank is filled with gasoline to a depth of exactly 2 feet. The tank is a cylinder resting horizontally on its side, with its circular ends oriented vertically. The inside of the tank is exactly 6 feet long. What is the volume of gasoline in the tank?

(1) The inside of the tank is exactly 4 feet in diameter.

(2) The top surface of the gasoline forms a rectangle that has an area of 24 square feet.

From OG 2016 (question 86 DS)

I get why 1 works, but the main qualm I have about 2 is how we can be sure that the 4 feet resulting from the square is a diameter of the circle ie. how we know that it fills the tank exactly up to halfway. Re: A tank is filled with gasoline to a depth of exactly 2 feet. The tank   [#permalink] 24 Nov 2019, 07:22

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