|
Author |
Message |
|
TAGS:
|
|
|
Intern
Joined: 29 Sep 2009
Posts: 16
|
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
24
This post was
BOOKMARKED
D
E
Question Stats:
38% (01:40) correct 62% (01:53) wrong based on 727 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.
Official Answer and Stats are available only to registered users. Register/ Login.
|
|
|
|
|
|
Manager
Joined: 02 Jan 2009
Posts: 86
Location: India
Schools: LBS
|
Re: Leak of water from the cone [#permalink]
Show Tags
07 Oct 2009, 01:53
(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.
_________________
The Legion dies, it does not surrender.
|
|
|
|
|
|
Math Expert
Joined: 02 Sep 2009
Posts: 44566
|
A right circular cone, twice as tall as it is wide at its [#permalink]
Show Tags
07 Oct 2009, 05:13
8
This post received
KUDOS
Expert's post
6
This post was
BOOKMARKED
jax91 wrote: (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 = \(9\pi=\pi*r^2\) --> \(r=3\) --> \(\frac{R}{H}=\frac{r}{h}=\frac{1}{4}\) --> \(h=12\) --> \(V=\frac{1}{3}*\pi*r^2*h=36*\pi\) 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. Attachment: 
Untitled.png [ 17.59 KiB | Viewed 8084 times ]
_________________
New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!
Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.
Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat
DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
|
|
|
|
|
|
Intern
Joined: 27 Jun 2011
Posts: 1
|
Re: Leak of water from the cone [#permalink]
Show Tags
30 Jun 2011, 23:03
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.
|
|
|
|
|
|
Intern
Joined: 29 Jun 2011
Posts: 12
Location: Ireland
|
Re: Leak of water from the cone [#permalink]
Show Tags
01 Jul 2011, 04:06
1
This post received
KUDOS
svikram wrote: 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.
_________________
http://www.testprepdublin.com
For the best GMAT, GRE, and SAT preparation.
|
|
|
|
|
|
Manager
Joined: 27 Dec 2011
Posts: 65
|
Re: A right circular cone, twice as tall as it is wide at its [#permalink]
Show Tags
19 Aug 2012, 01:28
hi Bunuel,
how did you get to the ratio:
R/H=r/h=1/4 ??
Can you please elaborate?
thanks!!
|
|
|
|
|
|
Manager
Joined: 04 Apr 2013
Posts: 140
|
Re: A right circular cone, twice as tall as it is wide at its [#permalink]
Show Tags
23 Jul 2013, 06:05
kartik222 wrote: hi Bunuel,
how did you get to the ratio:
R/H=r/h=1/4 ??
Can you please elaborate?
thanks!! kartik, similar triangle property... R/H = r/h since 2R=H r/h = 1/2 so h = 6.
_________________
Maadhu
MGMAT1 - 540 ( Trying to improve )
|
|
|
|
|
|
Manager
Status: Student
Joined: 26 Aug 2013
Posts: 233
Location: France
Concentration: Finance, General Management
GPA: 3.44
|
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" It could be 18pi/2 or 18pi/4! Where did i miss something? Plz explain! Thanks!
_________________
Think outside the box
|
|
|
|
|
|
Math Expert
Joined: 02 Sep 2009
Posts: 44566
|
Re: A right circular cone, twice as tall as it is wide at its [#permalink]
Show Tags
16 Nov 2013, 10:44
Paris75 wrote: 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"
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.
_________________
New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!
Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.
Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat
DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
|
|
|
|
|
|
Manager
Joined: 26 Sep 2013
Posts: 204
Concentration: Finance, Economics
GMAT 1: 670 Q39 V41 GMAT 2: 730 Q49 V41
|
Re: Leak of water from the cone [#permalink]
Show Tags
02 Dec 2013, 13:04
Bunuel wrote: jax91 wrote: (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?
|
|
|
|
|
|
Math Expert
Joined: 02 Sep 2009
Posts: 44566
|
Re: Leak of water from the cone [#permalink]
Show Tags
03 Dec 2013, 01:39
AccipiterQ wrote: Bunuel wrote: jax91 wrote: (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. Hope it's clear.
_________________
New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!
Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.
Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat
DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.
What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics
|
|
|
|
|
|
Intern
Joined: 02 Dec 2013
Posts: 7
|
Re: A right circular cone, twice as tall as it is wide at its [#permalink]
Show Tags
07 Dec 2013, 00:51
maaadhu wrote: kartik222 wrote: hi Bunuel,
how did you get to the ratio:
R/H=r/h=1/4 ??
Can you please elaborate?
thanks!! kartik, similar triangle property... R/H = r/h since 2R=H r/h = 1/2 so h = 6. I really find these problems very tough. Is there any reference to these problems ???
|
|
|
|
|
|
Non-Human User
Joined: 09 Sep 2013
Posts: 6639
|
Re: A right circular cone, twice as tall as it is wide at its [#permalink]
Show Tags
17 Mar 2018, 22:58
Hello from the GMAT Club BumpBot! Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos). Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
GMAT Books | GMAT Club Tests | Best Prices on GMAT Courses | GMAT Mobile App | Math Resources | Verbal Resources
|
|
|
|
|
|
|
Re: A right circular cone, twice as tall as it is wide at its
[#permalink]
17 Mar 2018, 22:58
|
|
|
|
|
|
|
|
|
|
|
