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# A right circular cylinder of 72 cubic meters is completely filled with

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A right circular cylinder of 72 cubic meters is completely filled with [#permalink]

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29 Nov 2014, 15:45
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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 $$\frac{6}{\sqrt{\pi}}$$ meters.

M07-26
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A right circular cylinder of 72 cubic meters is completely filled with [#permalink]

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Updated on: 27 Jan 2015, 19:49
1
The volume of a circular cylinder is V= πr^2h, so we know that πr^2h = 72 cubic meters. The cylinder is full, hence it holds 72000 liters.
Rate = 2 liters per hour per one square meter of surface
Work to be done equals to 30 liters. However, we need a square meter equivalent of the liters because we have a rate that is in square meters of surface. Hence, we cannot start answering the question unless we know the surface area. And in order to find the surface area we must know one of the variables r (radius) or h (height).
Once we know r or h we can plug one of them in the volume formula (πr^2h = 72) and use that info to find the surface area A=2πrh+2πr^2.

(1) Variable h. Sufficient.
(2) Variable r. Sufficient.

Originally posted by viktorija on 29 Nov 2014, 18:26.
Last edited by viktorija on 27 Jan 2015, 19:49, edited 3 times in total.
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Re: A right circular cylinder of 72 cubic meters is completely filled with [#permalink]

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30 Nov 2014, 00:53
davidfrank wrote:
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 meters.

hi, can you please check the highlighted portion of the question. i think you have missed some value, if not then answer cannot be D. it has to be A.
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Re: A right circular cylinder of 72 cubic meters is completely filled with [#permalink]

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30 Nov 2014, 05:46
1
davidfrank wrote:
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 $$\frac{6}{\sqrt{\pi}}$$ meters.

M07-26

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: $$2*\text{area}$$ will be the amount of water that evaporates each hour, thus $$\text{time}=\frac{30}{2*\text{area}}$$.

On the other hand since $$\text{volume}=\pi{r^2}h=72$$ then $$\text{area}=\pi{r^2}=\frac{72}{h}$$. 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. From this statement we have that $$\text{area}=\pi{r^2}=36$$. Sufficient.

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Re: A right circular cylinder of 72 cubic meters is completely filled with [#permalink]

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03 Dec 2014, 04:59
Bunuel wrote:
davidfrank wrote:
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 $$\frac{6}{\sqrt{\pi}}$$ meters.

M07-26

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: $$2*\text{area}$$ will be the amount of water that evaporates each hour, thus $$\text{time}=\frac{30}{2*\text{area}}$$.

On the other hand since $$\text{volume}=\pi{r^2}h=72$$ then $$\text{area}=\pi{r^2}=\frac{72}{h}$$. 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. From this statement we have that $$\text{area}=\pi{r^2}=36$$. Sufficient.

I have read your explanation but I couldn't follow it. How would the rate of evaporation be expressed.

2lts/hr/m^2..what I mean to say here is that when I express speed 100mph, I mean 100miles/1 hr
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Re: A right circular cylinder of 72 cubic meters is completely filled with [#permalink]

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03 Dec 2014, 06:49
davidfrank wrote:
Bunuel wrote:
davidfrank wrote:
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 $$\frac{6}{\sqrt{\pi}}$$ meters.

M07-26

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: $$2*\text{area}$$ will be the amount of water that evaporates each hour, thus $$\text{time}=\frac{30}{2*\text{area}}$$.

On the other hand since $$\text{volume}=\pi{r^2}h=72$$ then $$\text{area}=\pi{r^2}=\frac{72}{h}$$. 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. From this statement we have that $$\text{area}=\pi{r^2}=36$$. Sufficient.

I have read your explanation but I couldn't follow it. How would the rate of evaporation be expressed.

2lts/hr/m^2..what I mean to say here is that when I express speed 100mph, I mean 100miles/1 hr

Evaporation rate x is the amount of water that evaporates in 1 hour per square meter.
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Re: A right circular cylinder of 72 cubic meters is completely filled with [#permalink]

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04 Dec 2014, 03:20
Bunuel wrote:
davidfrank wrote:
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 $$\frac{6}{\sqrt{\pi}}$$ meters.

M07-26

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: $$2*\text{area}$$ will be the amount of water that evaporates each hour, thus $$\text{time}=\frac{30}{2*\text{area}}$$.

On the other hand since $$\text{volume}=\pi{r^2}h=72$$ then $$\text{area}=\pi{r^2}=\frac{72}{h}$$. 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. From this statement we have that $$\text{area}=\pi{r^2}=36$$. Sufficient.

Hi Bunuel

Sorry but I am unable to understand "two liters per hour per one square meter of surface"
why they have given this information and how to use it to calculate time?

eg. if we are given rate and distance we can find time=distance / rate
could you please explain in this terms, sorry to bother you but I am totally confused.

Thanks
Anupama
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Re: A right circular cylinder of 72 cubic meters is completely filled with [#permalink]

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04 Dec 2014, 06:36
2
Bunuel wrote:
davidfrank wrote:
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 $$\frac{6}{\sqrt{\pi}}$$ meters.

M07-26

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: $$2*\text{area}$$ will be the amount of water that evaporates each hour, thus $$\text{time}=\frac{30}{2*\text{area}}$$.

On the other hand since $$\text{volume}=\pi{r^2}h=72$$ then $$\text{area}=\pi{r^2}=\frac{72}{h}$$. 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. From this statement we have that $$\text{area}=\pi{r^2}=36$$. Sufficient.

Hi Bunuel

Sorry but I am unable to understand "two liters per hour per one square meter of surface"
why they have given this information and how to use it to calculate time?

eg. if we are given rate and distance we can find time=distance / rate
could you please explain in this terms, sorry to bother you but I am totally confused.

Thanks
Anupama

Water evaporates from the top of a pool, which is open. We are told that 2 liters evaporate from each square meter of surface per 1 hour.

So, 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.
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A right circular cylinder of 72 cubic meters is completely filled with [#permalink]

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26 Jan 2015, 18:28
Dear Bunuel, could you please tell me which form is correct to find the time? where I used this form 30/area/2 which is same form that you used in the below quetion but I found that in the above question you used different form which is 30/2*area. sorry about that but really I confused.

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?

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: \frac{area}{2} will be the amount of water that evaporates each hour, thus time=\frac{30}{(\frac{area}{2})}.

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.

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Re: A right circular cylinder of 72 cubic meters is completely filled with [#permalink]

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27 Jan 2015, 02:40
23a2012 wrote:
Dear Bunuel, could you please tell me which form is correct to find the time? where I used this form 30/area/2 which is same form that you used in the below quetion but I found that in the above question you used different form which is 30/2*area. sorry about that but really I confused.

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?

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: \frac{area}{2} will be the amount of water that evaporates each hour, thus time=\frac{30}{(\frac{area}{2})}.

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.

Correct solution is here: a-right-circular-cylinder-of-72-cubic-meters-is-completely-filled-with-189224.html#p1449175
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Re: A right circular cylinder of 72 cubic meters is completely filled with [#permalink]

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31 Oct 2015, 00:13
Dear Bunuel,

Please explain if this is correct? Total time is then = 30/2*area => 30/2*36 = 30/72=0.416 hour?

Many thanks again!

Bunuel wrote:
davidfrank wrote:
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 $$\frac{6}{\sqrt{\pi}}$$ meters.

M07-26

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: $$2*\text{area}$$ will be the amount of water that evaporates each hour, thus $$\text{time}=\frac{30}{2*\text{area}}$$.

On the other hand since $$\text{volume}=\pi{r^2}h=72$$ then $$\text{area}=\pi{r^2}=\frac{72}{h}$$. 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. From this statement we have that $$\text{area}=\pi{r^2}=36$$. Sufficient.

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Re: A right circular cylinder of 72 cubic meters is completely filled with [#permalink]

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31 Oct 2015, 03:42
Liza99 wrote:
Dear Bunuel,

Please explain if this is correct? Total time is then = 30/2*area => 30/2*36 = 30/72=0.416 hour?

Many thanks again!

Bunuel wrote:
davidfrank wrote:
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 $$\frac{6}{\sqrt{\pi}}$$ meters.

M07-26

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: $$2*\text{area}$$ will be the amount of water that evaporates each hour, thus $$\text{time}=\frac{30}{2*\text{area}}$$.

On the other hand since $$\text{volume}=\pi{r^2}h=72$$ then $$\text{area}=\pi{r^2}=\frac{72}{h}$$. 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. From this statement we have that $$\text{area}=\pi{r^2}=36$$. Sufficient.

______
Yes, that's correct.
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A right circular cylinder of 72 cubic meters is completely filled with [#permalink]

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31 Oct 2015, 12:29
2 Litre ----- 1 m^2 ------1 hour
72 Litre---- 36 m^2 -----36 hour [36 m^2 is the area that can be calculated from either 1 or 2]
30 Litre---- ---------------x

x = (30*36)/72

What is wrong with this Bunuel.

____________________________

Okay, I can see my error
The highlighted part will be 1 hour only
72 Litre ----------36 m^2-----------1 hour
30 Litre-------------------------------30/72=.416 hour

Am I right Bunuel ?
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Re: A right circular cylinder of 72 cubic meters is completely filled with [#permalink]

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31 Oct 2015, 20:35
Many thanks Bunuel as usual!!!
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Re: A right circular cylinder of 72 cubic meters is completely filled with [#permalink]

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01 Nov 2015, 00:51
Forget conventional ways of solving math questions. In DS, Variable approach is the easiest and quickest way to find the answer without actually solving the problem. Remember equal number of variables and independent equations ensures a 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, 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.

In the original condition, there are 2 variables (r,h) from rh=72, and we are given 2 conditions from the conditions when we only need one more equations to solve for the variables; there is high chance (D) will be our answer.
From condition 1, we get the area of the base when the height is given. As 2 liters are evaporated per square meter, we get get 30 liters from the ratio to the total evaporated liters. This is sufficient.
From condition 2, it is sufficient as condition 1, so the answer is (D).
There are many cases in which (D) is the answer when condition 1)=condition 2).

For cases where we need 1 more equation, such as original conditions with “1 variable”, or “2 variables and 1 equation”, or “3 variables and 2 equations”, we have 1 equation each in both 1) and 2). Therefore, there is 59 % chance that D is the answer, while A or B has 38% chance and C or E has 3% chance. Since D is most likely to be the answer using 1) and 2) separately according to DS definition. Obviously there may be cases where the answer is A, B, C or E.
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Re: A right circular cylinder of 72 cubic meters is completely filled with [#permalink]

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16 Feb 2017, 22:51
Another way to look at this problem in terms if units.

Only difficult part in this problem is to simplify this : " If water evaporates from the cylinder at a constant rate of two liters per hour per one square meter of surface."

So , above information is rate(R) and we know that Rate x Time = Word done.

R = $$\frac{2L}{hr/m^2}$$
==> $$\frac{2L}{hrm^2}$$ x Time = Word done(30L)

==> Time = $$\frac{30L m^2}{2L}$$ hr

Now cancel out L from Numerator and Denominator and in order to cancel $$m^2$$ we need to have area in denominator also so we will divide this expression by $$\pi r^2$$ $$m^2$$ (Since water is evaporating only from the open top surface,which is a circle)

So now Time = $$\frac{30}{2*\pi r^2}$$ hr----------(1)

V(72) = $$\pi r^2 h$$

St 1 : Height is given.We can calculate $$r^2$$ and replace this value in equation 1 - Sufficient.
St 2 : Radius is given directly. Sufficient .

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Re: A right circular cylinder of 72 cubic meters is completely filled with   [#permalink] 16 Feb 2017, 22:51
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