A right circular cylinder of 72 cubic meters

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A right circular cylinder of 72 cubic meters is completely filled with water. If water evaporates from the cylinder at a constant rate of two liters per hour per one square meter of surface, how long will it take for 30 liters of water to evaporate?

(1) The height of the cylinder is 2 meters.

(2) The radius of the base of the cylinder is 6/√π meters.

OA: D

HI Experts,

Can you please explain in detail?

Thanks
Nandish
Source: — Data Sufficiency |

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by ErikaPrepScholar » Thu Jan 18, 2018 6:38 am
We know the volume of the cylinder in question - 72 cubic meters. We need to find how long it takes for 30 liters to evaporate. HOWEVER, the rate of evaporation depends on the area of the surface of the water. This means we need to know the area of the surface - how big is the circle on top of the cylinder. We don't know this because our cylinder could have any proportions: our cylinder could be short and fat, tall and skinny, or somewhere in between, as long as it has a 72 cubic meter volume.

We know that the area of the circle must be A = πr^2. This means that if we know the radius of the cylinder, we can solve for area of the circle, which we can use to solve for rate of evaporation (rate = A in square meters * 2 liters/hour/square meter), which we can then use to solve for how long it will take to evaporate 30 liters. We also know that V = 72 = πr^2 * h, or because A = πr^2, V = 72 = A * h. This means that if we know the height of the cylinder, we can solve for area of the circle, then rate of evaporation, then length of time to evaporate 30 liters. So if we know either radius or height, the statement should be sufficient.

Statement 1 gives us height, so we know right away it is sufficient - no need to plug anything in. If we DID plug it in, we would get

$$72\ m^3=A\cdot2m$$ $$A=36m^2$$ $$36m^2\cdot2\frac{\frac{liters}{hour}}{m^2}$$ $$72\frac{liters}{hour}$$ $$\frac{30\ liters}{72\frac{liters}{hour}}=\frac{5}{12}hours$$

Statement 2 gives us radius, so it must be sufficient as well. But again, if we were to solve, we would get
$$A=\pi\left(\frac{6}{\sqrt{\pi}}m\right)^2=36m^2$$ $$36m^2\cdot2\frac{\frac{liters}{hour}}{m^2}$$ $$72\frac{liters}{hour}$$ $$\frac{30\ liters}{72\frac{liters}{hour}}=\frac{5}{12}hours$$

The correct answer is D.
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