An open-topped right circular cylinder with a volume of 72 cubic meter

Question

An open-topped right circular cylinder with a volume of 72 cubic meters is completely filled with water. Water evaporates from the cylinder at a constant rate of 2 liters per hour for every square meter of the top surface area. 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

viktorija · Accepted Answer

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.

Answer D

Bunuel · Answer

An open-topped right circular cylinder with a volume of 72 cubic meters is completely filled with water. Water evaporates from the cylinder at a constant rate of 2 liters per hour for every square meter of the top surface area. How long will it take for 30 liters of water to evaporate? 
 
To determine the time required for 30 liters of water to evaporate, we need to find the surface area of the top of the cylinder: the evaporation rate is  2 * area  liters per hour, so the time needed is  time = \frac{30}{2 *area} .
 
Since the volume of the cylinder is given by   volume= \pi{r^2}h = 72 , the top surface area is  	ext{area} = \pi{r^2} = \frac{72}{h} . Therefore, we need either the top surface area or the height of the cylinder to find the time required for evaporation.
 
(1) The height of the cylinder is 2 meters.
 
As discussed, this information is sufficient.
 
(2) The radius of the base of the cylinder is  \frac{6}{ \sqrt{\pi} }  meters. 
 
From this statement, we can calculate that the top surface area is  area = \pi{r^2} = 36 . This information is also sufficient.

Answer: D

manpreetsingh86 · Answer

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.

davidfrank · Answer

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

Bunuel · Answer

Evaporation rate x is the amount of water that evaporates in 1 hour per square meter.

anupamadw · Answer

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

Bunuel · Answer

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.

Liza99 · Answer

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 · Answer

______
Yes, that's correct.

keats · Answer

2 Litre ----- 1 m^2 ------1 hour
72 Litre---- 36 m^2 ----- 36 hour   
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  ?

Liza99 · Answer

Many thanks Bunuel as usual!!!

MathRevolution · Answer

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 \(\frac{6}{\sqrt{\pi}}\) meters.

M07-26

(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.

pranjal123 · Answer

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 .

Please +1 kudos If this post helps

dcummins · Answer

Took me a while to understand why we multiply 2 by the area in the denominator.

So for anyone else in the same boat here's what helped me in more clearer terms:

Time = Work/ Rate

Rate = 2litres per 1 square metre  of Surface  per 1 hour

Work = 30 litres

Therefore Time = 30 / (2 litres* X Square Metres of Surface)

X is what we determine and the missing piece of info.

bumpbot · Answer

Automated notice from GMAT Club BumpBot: 

A member just gave Kudos to this thread, showing it’s still useful. I’ve bumped it to the top so more people can benefit. Feel free to add your own questions or solutions.

 This post was generated automatically.

An open-topped right circular cylinder with a volume of 72 cubic meter

Prep Toolkit

Top 5 GMAT Debrief Videos

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards

GMAT Data Sufficiency (DS) Questions

An open-topped right circular cylinder with a volume of 72 cubic meter

Prep Toolkit

615 to 715 in 15 Days (Ria's Strategies)

More than Quant/Verbal Abilities: Speed vs. Accuracy

745 with Only Self-Prep and GMAT Club

From 555 to 765: 210-point Improvement

Perfect 805 Score Debrief by Julia

My Rewards