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,
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 \(2^2+(2\sqrt{3}-r)^2=r^2\)

.

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.

Answer (D)

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)