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A tank is filled with gasoline to a depth of exactly 2 feet. The tank

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

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New post 08 Apr 2018, 02:45
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)


[Reveal] Spoiler:
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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New post 09 Apr 2018, 02:08
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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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Re: A tank is filled with gasoline to a depth of exactly 2 feet. The tank [#permalink]

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New post 16 Apr 2018, 11:29
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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New post 17 Apr 2018, 00:26
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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] 17 Apr 2018, 00:26
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