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

There is a cylindrical tank with a diameter of 6 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 tank is filled with gasoline to a depth of exactly 2 feet.

(2) The top surface of the gasoline forms a rectangle that has an area of 34 square feet

Volume of a cylinder = \({pi}*r^2*h \)
Given h = 6; r=3

i) If gasoline is filled upto 2 ft would mean that it is filled upto \(\frac{1}{3}\) of the total volume
- Would be sufficient as we know height and radius and thus the volume of cylinder

ii) The top surface of the gasoline will change as the gasoline is filled in the tank (i.e. the vertical height - radius of the cylinder will change as gasoline is filled).
But the base will be same as the base of the cylinder i.e. 6.
Surface Area of the top = Base * Side
34 = 6 * Side => This side is not a diameter of the circle as the diameter of the circular end is 6

This side will thus be the chord of the circle formed by the top surface of the gasoline on the circular ends.

This chord will be same at 2 instances i.e. when gasoline is filled below the center of the circle and when it is filled above the diameter of the circle

Insufficient - as we can have 2 instances and the volume of gasoline in the instances would differ.

Answer - A
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Here, Diameter = 6 feet (Height of tank, lying horizontal) and Length of tank = 6 feet.

1) The tank is filled with gasoline to a depth of exactly 2 feet.
We can find the total volume (pi*radius 2 * h= 3.14*3*6=56.52) of the tank using the formula of volume of a cylinder. Tank having 6 feet height (diameter) have 56.52 volume, then tank having height of 2 will have 18.84 (56.52 * 2 /6) volume, which is volume of gasoline. So, Sufficient.

2) The top surface of the gasoline forms a rectangle that has an area of 34 square feet means area of the rectangle is 34.
If you see through the container from up above, the surface of the water will form a 2-d rectangle. We already know the length and width of the rectangle as we know diameter/length = 6 but we don't know the height of gasoline, So we can't find the volume of gasoline. Hence, Insufficient.

Ans. A

Given:
1. A tank is filled with gasoline to a depth of exactly 2 feet.
2. The tank is a cylinder resting horizontally on its side, with its circular ends oriented vertically.
3. The inside of the tank is exactly 6 feet long.

Asked: What is the volume of gasoline in the tank?

(1) The inside of the tank is exactly 6 feet in diameter.
Area can be derived
SUFFICIENT

(2) The top surface of the gasoline forms a rectangle that has an area of 34 square feet.
The top surface provides 2 possibilities for height H = 2 ft or 4 ft
NOT SUFFICIENT

The solution is provided in images below.
A separate image is used to calculate volume of gasoline in the tank.


IMO A

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There is a cylindrical tank with a diameter of 6 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 tank is filled with gasoline to a depth of exactly 2 feet.
(2) The top surface of the gasoline forms a rectangle that has an area of 34 square feet.

We're asked to calculate the volume of gasoline in the tank. Volume of gas = (cross-sectional-area) * (length). Since we know the horizontal length of the tank is 6 feet, we can (visually) simplify this problem to focus on the the dimensions of a circular segment. We know the overall area of the circle, from the diameter, but have no idea how full it is.

Let's simplify our statements:
(1) height of 2ft
(2) surface of gas is 36ft^2 --> chord length is 6 (since tank length is 6)

Since statement (1) tells us the height of the segment, and we know the radius and length of the tank, we COULD (but don't need to) use geometry to get eventually calculate much more about the circle and segment --> sufficient --> eliminate (b) and (c) and (e)

Statement (2) gives us the chord length of the surface of the gas. This also represents more data about the size of the segment, which can (through unnecessary geometry) tell us everything about the segment --> sufficient --> eliminate (a), answer is (d)

ANSWER :D
The question asks to find about the depth of the gasoline. Through depth, volume can be calculated.

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I am not sure about this solution, but let me give it a go. Remember a similar problem in OG like this, but a little different.

d=6, height off cylinger (length) = 6,

(1) height of gasoline is 2 ft. 2 ft is 1/3rd of the diameter. The problem here is if it was half of the diameter then we could have easily said \(\frac{1}{2}*\pi*r^2*h\). But it is 1/3rd. And it wont be 1/3rd as the 3 portions would be unequal (2 portions at either end would be same, the one at the middle is larger). Therefore with the tools i have, i do not think I can find out the exact area drawn by this secant. Probably there is a way, but since I cannot solve it now, I would say out.

(2) Similarly area of the rectangle is 34 sq. ft.
Which means \(\frac{34}{6} = 5\frac{2}{3}\) ft is the length of the secant. Same logic, if it was 6 ft, no problems. but since I do not have the tools to solve this, i would say out.

(1) + (2) Both statements are not giving me any extra information so I would say we cannot solve it.

IMO: E

only a can provide one answer, option B has two values .

Given the information in the question stem, we can find the volume of the cylindrical tank since we have the radius (3 feet) and the height (6 feet) of the tank. We need the the dimensions of the gasoline in the tank to be able to find its volume.
1) Since we know the depth of gasoline, we can figure out that the volume of gasoline would be 1/3 the total volume of the cylinder. So SUFFICIENT.
2) Since we know the height of the cylinder (6 feet), we can figure out the other side of the rectangle. Now, since we know the radius of the circle drawn straight down to the bottom of the cyclinder would split the side of the rectangle into equal halves. We can then figure out the distance between the top surface of the rectangle and the center of the circle using pythagoras theorem. Using this length, we can figure out the depth of the gasoline and hence the volume.
So SUFFICIENT.

Correct Answer: D

A & B alone are sufficient.
The diameter and the length of the tank are known to be 6 feet each. Moreover the tank is resting on its side, and is partially filled. Hence the gasoline will fill up a slice of a cylinder, akin to a 3D solid made out of the segment of a circle.
The only extra information needed to compute the volume of the gasoline in such a scenario is the height up to which the cylinder is filled.
If the height were known, we could find the area of the segment of the end-circle up till which gasoline is filled using the following formula:
Area Segment = Area Sector - Area Triangle (which can be computed by Pythagoras)
Thereafter we multiply by the known cylinder length to get the volume.
In the first option, the height is directly known, and that is sufficient.
In the second, we know that the top part of the gasoline forms a rectangle of a certain area. Given that we know the length of the cylinder, we can then find the length of the chord formed by the gasoline. From that information, the height up till which gasoline is filled can be derived. With that we can again compute volume.
Thus both options alone are sufficient

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I have a question here -
If the question stem or statement 2 would have mentioned that more than half of the cylinder is filled with gasoline, then, what would the answer be like?
As after that there would be only 1 instance possible right?
But in that case as well we would not be in position to calculate the numerical value of volume of gasoline so the answer should still remain the same ?

Bunuel Expert opinion please.

arya251294, I'm no expert but see if this helps -

Even if more than half the cylinder is filled with gas, I could see multiple volumes. If I look down from the top of the cylinder, I'd always see the same rectangle at the top (regardless of the height). It's is better to imagine this with water as opposed to gasoline, but the concept does not change.

I'm not sure of what formula will prove the above statements, but you'd see the same rectangle at multiple heights.

Why are you thinking of it as a gas?
Isn't gasoline liquid in the first place? I guess it is.

Also, if the question stem mentions that the cylinder is filled to more than half of its capacity, then, there could only be one set of data right? It doesn't matter what kind of rectangle I am able to see from top. What matters is calculation wise there is only one possibility left.

But the point of discussion is- in questions like these, when I am down to only one possibility but can't conclusively calculate the numerical value for my answer, then, shall that statement be considered sufficient or not?

1)
The calculations for the volume of the water at 2 feet can be very complicated but it's not necessary to actually calculate it.

We can reimagine the circular "sides" as bases and the "length" as the height of a solid object.



The green area is the depth of 2 feet. The green area * 6 feet long = volume of green liquid.

Center of diameter to top of green area = 1.
Center of diameter to where top of green area and circle intersect = 3 because they are the radius of the circle.

Now we can find the length of the top of the green area.

Now we can find the area shaded in red. You need to using trig functions to find exact values (as far as I can tell) but you don't need to actually do the calculation. If you really care, you can do cos^-1 (1/3) to get the angle between the radius going straight down and the radius going to where top of green and circle intersect. That will give you information to find the area of the sectors between the horizontal diameter and radii going to top of green.

Again, it's not necessary to calculate. You just need to know you can calculate it.

3*3*pi - area of red = area of green

Multiply area of green with 6 "horizontal height" and we get volume of green.

Sufficient

2)
The problem with this one is there are two heights possible: 1 when tank is more than half full, and 1 when tank is less than half full. To make sure this is insufficient, double check 34 isn't the area of the top rectangle when tank is exactly half full.

6*6=36, not=34. Confirming there are two possible volumes.

Insufficient.

very bad language in the text. Inside of the tank is 6 ft long = height of the cylinder? please correct the text, or at least indicate with ()

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See the official question : https://gmatclub.com/forum/a-tank-is-fi ... fl=similar




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