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water

by jainrahul1985 » Sat Feb 26, 2011 4:29 am
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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by anshumishra » Sat Feb 26, 2011 4:43 am
jainrahul1985 wrote: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
The rate of evaporation = 2 liters per hour per sq. meter
volume of water in the swimming pool = 56 m^3
Time to evaporate 30 liters of water from the swimming pool = ?

We need to find the surface area of the swimming pool to find this time.

Statement 1:
The depth of the pool is 2 meters

The surface area of the pool = volume / depth = 56/2 -- Sufficient

Statement 2:
The pool is circular with a radius of 3 meters

The surface area = pi*3*3 --- Sufficient

Hence, D
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Anshu

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by jainrahul1985 » Sat Feb 26, 2011 4:55 am
anshumishra wrote:
jainrahul1985 wrote: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
The rate of evaporation = 2 liters per hour per sq. meter
volume of water in the swimming pool = 56 m^3
Time to evaporate 30 liters of water from the swimming pool = ?

We need to find the surface area of the swimming pool to find this time.

Statement 1:
The depth of the pool is 2 meters

The surface area of the pool = volume / depth = 56/2 -- Sufficient

Statement 2:
The pool is circular with a radius of 3 meters

The surface area = pi*3*3 --- Sufficient

Hence, D
Thanks a ton for replying , but I am not sure what formulas have you used here .
For statement 2 why didn't you use : Surface Area of a Cylinder = 2 pi r^2 + 2 pi r h

Also I didn't get the formula used in Statement 1 .
Please help me understand .
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by gmatmachoman » Sat Feb 26, 2011 5:01 am
Area covered : Pi r^2 + pi *r * h + Pi *r * h

St 1:

We are not sure whether it's a cuboid or a cylindrical structure

Insufficient

St 2 :

Radius is given ,volume is given . So we can find height. And thereby we can find the covered surface area.

Sufficient.

IMO B.
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by jainrahul1985 » Sat Feb 26, 2011 5:04 am
OA D
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by gmatmachoman » Sat Feb 26, 2011 5:07 am
jainrahul1985 wrote:OA D
Then in that case, one needs to assume the given swimming pool is cylindrical only.

Wish experts reply for this one...

but these days, geometrical questions has changed way beyond common mensurations stuff!!
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by anshumishra » Sat Feb 26, 2011 5:10 am
jainrahul1985 wrote: Thanks a ton for replying , but I am not sure what formulas have you used here .
For statement 2 why didn't you use : Surface Area of a Cylinder = 2 pi r^2 + 2 pi r h
Formula used :
Volume = area of the base * height

(So, even if you have the shape of base such as square, triangle, circular, or ploygon, this would work).
In fact using this formula, I can derived the volume of a cylindrical pond as = area of the base * height = (pi*r^2) * h -- which you already know as right.
Also I didn't get the formula used in Statement 1 .
Same formula : area of the base = volume/ depth.
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by anshumishra » Sat Feb 26, 2011 5:16 am
jainrahul1985 wrote: For statement 2 why didn't you use : Surface Area of a Cylinder = 2 pi r^2 + 2 pi r h
The pond (lets say for now), is open. The area 2 pi r^2 + 2 pi r h is the area of the two circular faces (say the top and the bottom part = 2*pi*r^2) and the surface of the sides (2*pi*r*h). We are not interested in that area.

The water is evaporated because the lower surface is warm, hence the only area we are concerned is the circular area of the bottom of the cylindrical pond = pi*r^2

Hope that helps !
Thanks
Anshu

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