Water evaporates at the rate of two liters per hour per one square meter of surface. How long will it take to evaporate 30 liters of water from a swimming pool full of water with vertical walls and a flat bottom that holds 56 cubic meters of water?

1. The depth of the pool is 2 meters
2. The pool is circular with a radius of 3 meters


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D

We need to calculate surface area, since the walls are vertical, the surface area is same at base and at the water level.

Statement 1 : Area = volume / height --> Suff
Statement 2 : Area = pi * 3^2 --> Suff

OA is D.
Can you explain the rest of the calculation, I don't get how we can solve the problem.
Thanks

Yes , answer can be calculated using both statements individually. So I will go with D
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In case of DS question we should just check if we can get the ans, that is if we have all the suffient data to solve the problem . We are not required to get the actual answer.
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i got same Ans: D

area=volume/hight
so s1 and s2 both suff.
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MBA (Mind , Body and Attitude )

At first I chose B.

Thanks for clear explanation.

From stmt 1, how do we know the pool is in cylindrical shape?

V=a*b*c

a, b, c - linear sizes of the pool
if we are given its depth (say "c"), we can find a*b. This is the surface.
Exactly what we need.

In 1) we consider the shape to be a parallelepiped.

This question has minor discrepancies. This reminded me of Units and Dimensions from Physics.

Rate of evaporation = Volume of water evaporated/(Time*Surface Area occupied by the water evaporated)

Time = Volume of water evaporated/(Rate of evaporation*Total Surface Area occupied by the water evaporated)

Volume of water evaporated=30 liters
Rate of evaporation = 2 l/(h*m^2)
Total Surface Area = ?
Time = (30/(2*Area)) hours = (15/Area) hours

Q: What is the total surface area of the water occupied by the water evaporated?

1. The depth of the pool is 2 meters
We don't know the shape of the pool and at least the information about the shape of the pool is required to find the area. We may require few more information but certainly this is insufficient.
The shape of the pool may be cylinder, rectangular box, triangular prism, pentagonal prism, cube. Note: the shape can't be conical as the walls are vertical and a cone is slanting.
Not Sufficient.

2.
The pool is circular with a radius of 3 meters.
We now know that the pool is cylindrical in shape and the radius of the cylinder=3m

The volume of water to be evaporated = 30l
1 liter=10^{-3} m^3
30 liters=30*10^{-3} m^3 = 0.03 m^3

Volume of a cylinder = \pi*r^2*h
0.03 = \pi*3^2*h

h = \frac{0.03}{9*\pi} = \frac{0.01}{3*\pi} m

Now, we have the height of the water evaporated and also the radius of the water evaporated. We can find the total surface area.

Area = 2*\pi*r(r+h)
r=3 meters
h = \frac{0.01}{3*\pi} meters
Sufficient.

Ans: "B"
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I don't think that the two statements contradict each other. But in my opinion, the answer is not "D". According to our finding, the swimming pool is a cylinder. Pool's radius=3m and height=2m.

Stem says; volume of the pool=56 cubic meter
\pi*r^2*h=\pi*3^2*2=\pi*18 \approx 56. Yes, I still don't like this approximate value though.
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~fluke

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