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A right circular cylinder

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A right circular cylinder [#permalink] New post 15 Jul 2012, 11:48
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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 6π√ meters.
[Reveal] Spoiler: OA
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Re: A right circular cylinder [#permalink] New post 15 Jul 2012, 11:55
I don't understand the highlighted portion of the explanation.



To find the time needed for 30 liters of water to evaporate we need to find the surface area of the top of the cylinder: area/2 will be the amount of water that evaporates each hour, thus time=30/(area/2).


On the other hand since volume=π(r^2)h=72 then area=π(r^2)=72/h. So, basically all we need is ether the area of the surface or the height of the cylinder.

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

(2) The radius of the base of the cylinder is 6/√π meters. From this statement we have that area=π(r^2)=36. Sufficient.
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Re: A right circular cylinder [#permalink] New post 16 Jul 2012, 05:11
Expert's post
santivilla wrote:
I don't understand the highlighted portion of the explanation.



To find the time needed for 30 liters of water to evaporate we need to find the surface area of the top of the cylinder: area/2 will be the amount of water that evaporates each hour, thus time=30/(area/2).


On the other hand since volume=π(r^2)h=72 then area=π(r^2)=72/h. So, basically all we need is ether the area of the surface or the height of the cylinder.

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

(2) The radius of the base of the cylinder is 6/√π meters. From this statement we have that area=π(r^2)=36. Sufficient.


It should be: To find the time needed for 30 liters of water to evaporate we need to find the surface area of the top of the cylinder: 2*area will be the amount of water that evaporates each hour, thus time=\frac{30}{2*area}.

For example if the surface area of the top is 5m^2, then in one hour 5*2=10 liters of water evaporates hence it'll take 30/10=3 hours 30 liters of water to evaporate.

Complete solution.

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 of the top, how long will it take for 30 liters of water to evaporate?

To find the time needed for 30 liters of water to evaporate we need to find the surface area of the top of the cylinder: 2*area will be the amount of water that evaporates each hour, thus time=\frac{30}{2*area}.

On the other hand since volume=\pi{r^2}h=72 then area=\pi{r^2}=\frac{72}{h}. So, basically all we need is ether the area of the surface or the height of the cylinder.

(1) The height of the cylinder is 2 meters. Sufficient.
(2) The radius of the base of the cylinder is \frac{6}{\sqrt{\pi}} meters --> area=\pi{r^2}=36. Sufficient.

Answer: D.
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Re: A right circular cylinder [#permalink] New post 06 Dec 2013, 23:54
santivilla wrote:
I don't understand the highlighted portion of the explanation.



To find the time needed for 30 liters of water to evaporate we need to find the surface area of the top of the cylinder: area/2 will be the amount of water that evaporates each hour, thus time=30/(area/2).


On the other hand since volume=π(r^2)h=72 then area=π(r^2)=72/h. So, basically all we need is ether the area of the surface or the height of the cylinder.

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

(2) The radius of the base of the cylinder is 6/√π meters. From this statement we have that area=π(r^2)=36. Sufficient.


That was really very good question. I wish I could answer that!!! lol
Re: A right circular cylinder   [#permalink] 06 Dec 2013, 23:54
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