Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized for You

we will pick new questions that match your level based on your Timer History

Track Your Progress

every week, we’ll send you an estimated GMAT score based on your performance

Practice Pays

we will pick new questions that match your level based on your Timer History

Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.

It appears that you are browsing the GMAT Club forum unregistered!

Signing up is free, quick, and confidential.
Join other 500,000 members and get the full benefits of GMAT Club

Registration gives you:

Tests

Take 11 tests and quizzes from GMAT Club and leading GMAT prep companies such as Manhattan GMAT,
Knewton, and others. All are free for GMAT Club members.

Applicant Stats

View detailed applicant stats such as GPA, GMAT score, work experience, location, application
status, and more

Books/Downloads

Download thousands of study notes,
question collections, GMAT Club’s
Grammar and Math books.
All are free!

Thank you for using the timer!
We noticed you are actually not timing your practice. Click the START button first next time you use the timer.
There are many benefits to timing your practice, including:

A right circular cone, twice as tall as it is wide at its [#permalink]

Show Tags

07 Oct 2009, 00:31

3

This post received KUDOS

22

This post was BOOKMARKED

00:00

A

B

C

D

E

Difficulty:

95% (hard)

Question Stats:

35% (01:42) correct
65% (01:50) wrong based on 748 sessions

HideShow timer Statistics

A right circular cone, twice as tall as it is wide at its greatest width, is pointing straight down. The cone is partially filled with water, which is dripping out of a tiny hole in the cone's tip at a rate of 2 cubic centimeters per hour. If the water were to continue to drip out at this rate, how much longer would it take for the cone to empty, assuming that no water is added to the cone and that there is no loss of water from the cone by any other means?

(1) The top surface of the water in the cone is currently \(9\pi\) square centimeters in area. (2) The top surface of the water in the cone currently is exactly 4 centimeters below the cone's top, measuring vertically.

(1) The top surface of the water in the cone is currently 9pi square centimeters in area. -- sufficient on its own (we can get D) (2) The top surface of the water in the cone currently is exactly 4 centimeters below the cone's top, measuring vertically. -- sufficient on its own ( we have H)

As the ratio of diameter:hieght of any sub-cone formed in this cone will be 1:2

(1) The top surface of the water in the cone is currently 9pi square centimeters in area. -- sufficient on its own (we can get D) (2) The top surface of the water in the cone currently is exactly 4 centimeters below the cone's top, measuring vertically. -- sufficient on its own ( we have H)

As the ratio of diameter:hieght of any sub-cone formed in this cone will be 1:2

So we need either D or H to get the volume.

IMO D.

Disagree.

A right circular cone, twice as tall as it is wide at its greatest width, is pointing straight down. The cone is partially filled with water, which is dripping out of a tiny hole in the cone's tip at a rate of 2 cubic centimeters per hour. If the water were to continue to drip out at this rate, how much longer would it take for the cone to empty, assuming that no water is added to the cone and that there is no loss of water from the cone by any other means?

Attachment:

Untitled.png [ 17.59 KiB | Viewed 6985 times ]

H - height of cone, R radius of cone. h - height of water in cone, r radius of top surface of water in cone.

(1) The top surface of the water in the cone is currently \(9\pi\) square centimeters in area. Top surface area of water = \(9\pi=\pi*r^2\) --> \(r=3\) --> \(\frac{R}{H}=\frac{r}{h}=\frac{1}{4}\) --> \(h=12\) --> \(V=\frac{1}{3}*\pi*r^2*h=36*\pi\) cubic centimeters.

Leak rate 2 cubic centimeters per hour --> \(time=\frac{36\pi}{2}\) hours.

Sufficient.

(2) The top surface of the water in the cone currently is exactly 4 centimeters below the cone's top, measuring vertically. Not sufficient we know that H=h+4, but h can be any value and thus the Volume can be any.

It cant be A cause the question says, e cone is partially filled with water.

A can be true only when the cone is fully filled.

If we know the ratio for height:width for any volume in a cone, then that ratio applies to all volumes. This rule is due to the fact that the angles in the cone stay constant when the volume changes. Statement 1 gives us the area at the top of the water. This allows us to find the water volume, using the height:width ratio provided, and subsequently the rate of leaking. A is the answer.
_________________

Re: A right circular cone, twice as tall as it is wide at its [#permalink]

Show Tags

27 Jul 2012, 23:16

Answer must be (E) as no statements individually can give either the value of radius 'r' or height 'h'

Time required (in minutes) to empty the cone = (60/2)* pie * r^2*h h= 4r

1) Now the original question states that the cone is "partially filled" & not full filled. Thus statement 1 won't suffice. 2) Water level is 4 cm below the full height - Thus not sufficient.

1+2) hr= 3h + 4, which is still insufficient .

Thus the answer is E
_________________

If you like my Question/Explanation or the contribution, Kindly appreciate by pressing KUDOS. Kudos always maximizes GMATCLUB worth-Game Theory

If you have any question regarding my post, kindly pm me or else I won't be able to reply

Answer must be (E) as no statements individually can give either the value of radius 'r' or height 'h'

Time required (in minutes) to empty the cone = (60/2)* pie * r^2*h h= 4r

1) Now the original question states that the cone is "partially filled" & not full filled. Thus statement 1 won't suffice. 2) Water level is 4 cm below the full height - Thus not sufficient.

(1) The top surface of the water in the cone is currently 9pi square centimeters in area. -- sufficient on its own (we can get D) (2) The top surface of the water in the cone currently is exactly 4 centimeters below the cone's top, measuring vertically. -- sufficient on its own ( we have H)

As the ratio of diameter:hieght of any sub-cone formed in this cone will be 1:2

So we need either D or H to get the volume.

IMO D.

Disagree.

A right circular cone, twice as tall as it is wide at its greatest width, is pointing straight down. The cone is partially filled with water, which is dripping out of a tiny hole in the cone's tip at a rate of 2 cubic centimeters per hour. If the water were to continue to drip out at this rate, how much longer would it take for the cone to empty, assuming that no water is added to the cone and that there is no loss of water from the cone by any other means?

H - height of cone, R radius of cone. h - height of water in cone, r radius of top surface of water in cone.

(1) The top surface of the water in the cone is currently \(9\pi\) square centimeters in area. Top surface area of water=9pi=pi*r^2 --> r=3 --> R/H=r/h=1/4 --> h=12 --> V=1/3*pi*r^2*h=36*pi

Leak rate 2 cubic centimeters per hour --> 36pi/2

Sufficient

(2) The top surface of the water in the cone currently is exactly 4 centimeters below the cone's top, measuring vertically. Not sufficient we know that H=h+4, but h can be any value and thus the Volume can be any.

Answer: A.

Hello Bunuel,

For the second statement , we have the depth of the cone as 4 cms which implies that the Width of the water in the cone at that point is 2cm: Implying the radius to be 1 cm and ; from this the volume of water in the cone can be derived and also the leak rate.

Re: A right circular cone, twice as tall as it is wide at its [#permalink]

Show Tags

15 Nov 2013, 16:02

Hi,

have a small question: it is stated that "The cone is partially filled with water, which is dripping out of a tiny hole in the cone's tip at a rate of 2 cubic centimeters per hour"

It has been said that : the leak rate 2 cubic centimeters per hour --> 36pi/2. Meaning that it will take 18pi hours to fill the cone.

But, the cone could be half full. or 3/4 full. We don't know!

Therefore, the result will be different since they ask : "how much longer would it take for the cone to empty, assuming that no water is added to the cone and that there is no loss of water from the cone by any other means"

have a small question: it is stated that "The cone is partially filled with water, which is dripping out of a tiny hole in the cone's tip at a rate of 2 cubic centimeters per hour"

It has been said that : the leak rate 2 cubic centimeters per hour --> 36pi/2. Meaning that it will take 18pi hours to fill the cone.

But, the cone could be half full. or 3/4 full. We don't know!

Therefore, the result will be different since they ask : "how much longer would it take for the cone to empty, assuming that no water is added to the cone and that there is no loss of water from the cone by any other means"

It could be 18pi/2 or 18pi/4!

Where did i miss something? Plz explain!

Thanks!

\(36\pi\) is the volume of water in the cone not the total volume of the cone.
_________________

(1) The top surface of the water in the cone is currently 9pi square centimeters in area. -- sufficient on its own (we can get D) (2) The top surface of the water in the cone currently is exactly 4 centimeters below the cone's top, measuring vertically. -- sufficient on its own ( we have H)

As the ratio of diameter:hieght of any sub-cone formed in this cone will be 1:2

So we need either D or H to get the volume.

IMO D.

Disagree.

A right circular cone, twice as tall as it is wide at its greatest width, is pointing straight down. The cone is partially filled with water, which is dripping out of a tiny hole in the cone's tip at a rate of 2 cubic centimeters per hour. If the water were to continue to drip out at this rate, how much longer would it take for the cone to empty, assuming that no water is added to the cone and that there is no loss of water from the cone by any other means?

Attachment:

Untitled.png

H - height of cone, R radius of cone. h - height of water in cone, r radius of top surface of water in cone.

(1) The top surface of the water in the cone is currently \(9\pi\) square centimeters in area. Top surface area of water = \(9\pi=\pi*r^2\) --> \(r=3\) --> \(\frac{R}{H}=\frac{r}{h}=\frac{1}{4}\) --> \(h=12\) --> \(V=\frac{1}{3}*\pi*r^2*h=36*\pi\) cubic centimeters.

Leak rate 2 cubic centimeters per hour --> \(time=\frac{36\pi}{2}\) hours.

Sufficient.

(2) The top surface of the water in the cone currently is exactly 4 centimeters below the cone's top, measuring vertically. Not sufficient we know that H=h+4, but h can be any value and thus the Volume can be any.

Answer: A.

The top surface of the water in the cone is currently \(9\pi\) square centimeters in area. Top surface area of water = \(9\pi=\pi*r^2\) --> \(r=3\) --> \(\frac{R}{H}=\frac{r}{h}=\frac{1}{4}\)

(1) The top surface of the water in the cone is currently 9pi square centimeters in area. -- sufficient on its own (we can get D) (2) The top surface of the water in the cone currently is exactly 4 centimeters below the cone's top, measuring vertically. -- sufficient on its own ( we have H)

As the ratio of diameter:hieght of any sub-cone formed in this cone will be 1:2

So we need either D or H to get the volume.

IMO D.

Disagree.

A right circular cone, twice as tall as it is wide at its greatest width, is pointing straight down. The cone is partially filled with water, which is dripping out of a tiny hole in the cone's tip at a rate of 2 cubic centimeters per hour. If the water were to continue to drip out at this rate, how much longer would it take for the cone to empty, assuming that no water is added to the cone and that there is no loss of water from the cone by any other means?

Attachment:

Untitled.png

H - height of cone, R radius of cone. h - height of water in cone, r radius of top surface of water in cone.

(1) The top surface of the water in the cone is currently \(9\pi\) square centimeters in area. Top surface area of water = \(9\pi=\pi*r^2\) --> \(r=3\) --> \(\frac{R}{H}=\frac{r}{h}=\frac{1}{4}\) --> \(h=12\) --> \(V=\frac{1}{3}*\pi*r^2*h=36*\pi\) cubic centimeters.

Leak rate 2 cubic centimeters per hour --> \(time=\frac{36\pi}{2}\) hours.

Sufficient.

(2) The top surface of the water in the cone currently is exactly 4 centimeters below the cone's top, measuring vertically. Not sufficient we know that H=h+4, but h can be any value and thus the Volume can be any.

Answer: A.

The top surface of the water in the cone is currently \(9\pi\) square centimeters in area. Top surface area of water = \(9\pi=\pi*r^2\) --> \(r=3\) --> \(\frac{R}{H}=\frac{r}{h}=\frac{1}{4}\)

after you solved for r=3, how did you get

\(\frac{R}{H}=\frac{r}{h}=\frac{1}{4}\)

Aren't R, H, and h, all unknown?

We are given that the cone, twice as tall as it is wide, which means that H = 2D --> H = 4R --> R/H = 1/4. Because of similar triangles, the same applies to r and h.

(1) The top surface of the water in the cone is currently 9pi square centimeters in area. -- sufficient on its own (we can get D) (2) The top surface of the water in the cone currently is exactly 4 centimeters below the cone's top, measuring vertically. -- sufficient on its own ( we have H)

As the ratio of diameter:hieght of any sub-cone formed in this cone will be 1:2

So we need either D or H to get the volume.

IMO D.

Disagree.

A right circular cone, twice as tall as it is wide at its greatest width, is pointing straight down. The cone is partially filled with water, which is dripping out of a tiny hole in the cone's tip at a rate of 2 cubic centimeters per hour. If the water were to continue to drip out at this rate, how much longer would it take for the cone to empty, assuming that no water is added to the cone and that there is no loss of water from the cone by any other means?

Attachment:

Untitled.png

H - height of cone, R radius of cone. h - height of water in cone, r radius of top surface of water in cone.

(1) The top surface of the water in the cone is currently \(9\pi\) square centimeters in area. Top surface area of water = \(9\pi=\pi*r^2\) --> \(r=3\) --> \(\frac{R}{H}=\frac{r}{h}=\frac{1}{4}\) --> \(h=12\) --> \(V=\frac{1}{3}*\pi*r^2*h=36*\pi\) cubic centimeters.

Leak rate 2 cubic centimeters per hour --> \(time=\frac{36\pi}{2}\) hours.

Sufficient.

(2) The top surface of the water in the cone currently is exactly 4 centimeters below the cone's top, measuring vertically. Not sufficient we know that H=h+4, but h can be any value and thus the Volume can be any.

Answer: A.

Would you please remind me why you divided by 3 in volume calc?

We’ve given one of our favorite features a boost! You can now manage your profile photo, or avatar , right on WordPress.com. This avatar, powered by a service...

Sometimes it’s the extra touches that make all the difference; on your website, that’s the photos and video that give your content life. You asked for streamlined access...

Post today is short and sweet for my MBA batchmates! We survived Foundations term, and tomorrow's the start of our Term 1! I'm sharing my pre-MBA notes...

“Keep your head down, and work hard. Don’t attract any attention. You should be grateful to be here.” Why do we keep quiet? Being an immigrant is a constant...