Check GMAT Club Decision Tracker for the Latest School Decision Releases https://gmatclub.com/AppTrack

 It is currently 28 Apr 2017, 16:46

### GMAT Club Daily Prep

#### 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

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

# Events & Promotions

###### Events & Promotions in June
Open Detailed Calendar

# A 10-by-6 inch piece of paper is used to form the lateral surface of a

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 28 Aug 2010
Posts: 262
Followers: 6

Kudos [?]: 640 [0], given: 11

A 10-by-6 inch piece of paper is used to form the lateral surface of a [#permalink]

### Show Tags

10 Jan 2011, 19:00
12
This post was
BOOKMARKED
00:00

Difficulty:

65% (hard)

Question Stats:

55% (02:21) correct 45% (01:12) wrong based on 330 sessions

### HideShow timer Statistics

A 10-by-6 inch piece of paper is used to form the lateral surface of a cylinder. If the entire piece of paper is used to make the lateral surface, which of the following must be true of the two possible cylinders that can be formed?

A. The volume of the cylinder with height 10 is $$\frac{60}{\pi}$$ cubic inches greater than the volume of the cylinder with height 6.

B. The volume of the cylinder with height 6 is $$\frac{60}{\pi}$$ cubic inches greater than the volume of the cylinder with height 10.

C. The volume of the cylinder with height 10 is $$60\pi$$ cubic inches greater than the volume of the cylinder with height 6.

D. The volume of the cylinder with height 6 is $$60\pi$$ cubic inches greater than the volume of the cylinder with height 10.

E. The volume of the cylinder with height 6 is $$\frac{240}{\pi}$$ cubic inches greater than the volume of the cylinder with height 10.
[Reveal] Spoiler: OA

_________________

Gmat: everything-you-need-to-prepare-for-the-gmat-revised-77983.html
-------------------------------------------------------------------------------------------------
Ajit

Last edited by Bunuel on 02 Jan 2017, 04:55, edited 2 times in total.
Edited the question
Intern
Joined: 08 Jun 2010
Posts: 10
Followers: 0

Kudos [?]: 3 [0], given: 1

Re: A 10-by-6 inch piece of paper is used to form the lateral surface of a [#permalink]

### Show Tags

10 Jan 2011, 20:11
1
This post was
BOOKMARKED
Simple math
2. Find volume (pi)*r^2*h of each
case a: 2(pi)r =10 and h = 6 --> (pi)r^2*h = (pi) [10/2*(pi)]^2 * 6 = 25*6/(pi) = 150/pi
case b: 2(pi)r =6 and h = 10 --> (pi)r^2*h = (pi) [6/2*(pi)]^2 * 10 = 9*10/(pi) = 90/pi
3. Difference is 60/pi
4. So [case a volume] when h = 6 is greater than [case b volume ] when h = 10, by 60/(pi)
Intern
Affiliations: CFA Charterholder
Joined: 25 Oct 2010
Posts: 25
Schools: EWMBA Haas
Followers: 0

Kudos [?]: 4 [0], given: 5

Re: A 10-by-6 inch piece of paper is used to form the lateral surface of a [#permalink]

### Show Tags

28 Jul 2011, 09:34
2
This post was
BOOKMARKED
A 10-by-6 inch piece of paper is used to form the lateral surface of a cylinder. If the entire piece of paper is used to make the lateral surface, which of the following must be true of the two possible cylinders that can be formed?

A The volume of the cylinder with height 10 is 60/pi cubic inches greater than the volume of the cylinder with height 6.

B The volume of the cylinder with height 6 is 60/pi cubic inches greater than the volume of the cylinder with height 10.

C The volume of the cylinder with height 10 is 60pi cubic inches greater than the volume of the cylinder with height 6.

D The volume of the cylinder with height 6 is 60pi cubic inches greater than the volume of the cylinder with height 10.

E The volume of the cylinder with height 6 is 240/pi cubic inches greater than the volume of the cylinder with height 10.
Senior Manager
Joined: 30 Aug 2009
Posts: 286
Location: India
Concentration: General Management
Followers: 3

Kudos [?]: 168 [0], given: 5

Re: A 10-by-6 inch piece of paper is used to form the lateral surface of a [#permalink]

### Show Tags

28 Jul 2011, 12:24
baker2145 wrote:
Here's the question:

A 10-by-6 inch piece of paper is used to form the lateral surface of a cylinder. If the entire piece of paper is used to make the lateral surface, which of the following must be true of the two possible cylinders that can be formed?

A The volume of the cylinder with height 10 is 60/pi cubic inches greater than the volume of the cylinder with height 6.

B The volume of the cylinder with height 6 is 60/pi cubic inches greater than the volume of the cylinder with height 10.

C The volume of the cylinder with height 10 is 60pi cubic inches greater than the volume of the cylinder with height 6.

D The volume of the cylinder with height 6 is 60pi cubic inches greater than the volume of the cylinder with height 10.

E The volume of the cylinder with height 6 is 240/pi cubic inches greater than the volume of the cylinder with height 10.

I am having difficulty with this one: Please help and explain, if answer if B or E, WHY it is (#/pi) and not #pi, considering pi(r-squared)(h) is the volume formula

Thanks,

6 or 10 will be circumference ...so 2 * pi* r = 6 or 10 and hence r = #/pi....and difference would be 60/pi [applying the volume formula and taking the difference] ...would go with B
Intern
Joined: 27 Feb 2011
Posts: 48
Followers: 0

Kudos [?]: 3 [0], given: 9

Re: A 10-by-6 inch piece of paper is used to form the lateral surface of a [#permalink]

### Show Tags

28 Jul 2011, 12:58
when the paper is folded with the 10 as the height .. 6 will be the circumference not the radius.. so 2*pi*r = 6 -> r = 3/ pi.. then its pretty straightforward.. pi ( r1*r1*h1 - r2*r2*h)
Intern
Joined: 18 Jul 2011
Posts: 49
Followers: 3

Kudos [?]: 18 [2] , given: 2

Re: A 10-by-6 inch piece of paper is used to form the lateral surface of a [#permalink]

### Show Tags

28 Jul 2011, 13:05
2
KUDOS
1
This post was
BOOKMARKED
baker2145 wrote:
Here's the question:

A 10-by-6 inch piece of paper is used to form the lateral surface of a cylinder. If the entire piece of paper is used to make the lateral surface, which of the following must be true of the two possible cylinders that can be formed?

A The volume of the cylinder with height 10 is 60/pi cubic inches greater than the volume of the cylinder with height 6.

B The volume of the cylinder with height 6 is 60/pi cubic inches greater than the volume of the cylinder with height 10.

C The volume of the cylinder with height 10 is 60pi cubic inches greater than the volume of the cylinder with height 6.

D The volume of the cylinder with height 6 is 60pi cubic inches greater than the volume of the cylinder with height 10.

E The volume of the cylinder with height 6 is 240/pi cubic inches greater than the volume of the cylinder with height 10.

I am having difficulty with this one: Please help and explain, if answer if B or E, WHY it is (#/pi) and not #pi, considering pi(r-squared)(h) is the volume formula

Thanks,

Hopefully, you have some intuition about which of the possible cylinders is going to have the greater volume. Because the volume of a cylinder is directly proportional to the height and directly proportional to the square of the radius, the size of the radius has the greatest effect on the volume of the cylinder. Given this intuition we can eliminate A and C.

The answer given already is correct, but I'm going to provide some more details in term of calculation

Cylinder with height 10 and circumference 6:
$$2pi(r) = 6$$
$$r = \frac{3}{(pi)}$$
$$V = (pi)(\frac{3}{pi})^2(10)$$
$$V = \frac{90}{pi}$$

Cylinder with height 6 and circumference 10:
$$2pi(r) = 10$$
$$r = \frac{5}{(pi)}$$
$$V = (pi)(\frac{5}{pi})^2(6)$$
$$V = \frac{150}{pi}$$

150-90 = 60

So, B.
Manager
Status: Post application wait begins!
Joined: 15 Aug 2010
Posts: 145
Location: United States (CA)
Concentration: Strategy, Technology
GMAT 1: 720 Q50 V37
GPA: 3.82
WE: Engineering (Computer Software)
Followers: 2

Kudos [?]: 12 [0], given: 3

Re: A 10-by-6 inch piece of paper is used to form the lateral surface of a [#permalink]

### Show Tags

31 Jul 2011, 23:32
Pretty straightforward. Plug in the values to compute the volume of the cylinder. Keep in mind 6 and 10 are the circumference of the base and not the radius. B is the right answer.
_________________

Give me kudos if you like my post!

Manager
Joined: 27 Feb 2012
Posts: 136
Followers: 1

Kudos [?]: 53 [0], given: 22

Re: A 10-by-6 inch piece of paper is used to form the lateral surface of a [#permalink]

### Show Tags

28 Feb 2013, 13:24
mun23 wrote:
A 10-by-6 inch piece of paper is used to form the lateral surface of a cylinder. If the entire piece of paper is used to make the lateral surface, which of the following must be true of the two possible cylinders that can be formed?

(A)The volume of the cylinder with height 10 is 60 / cubic inches greater than the volume of the cylinder with height 6.

(B)The volume of the cylinder with height 6 is 60 / cubic inches greater than the volume of the cylinder with height 10.

(C)The volume of the cylinder with height 10 is 60 cubic inches greater than the volume of the cylinder with height 6.

(D)The volume of the cylinder with height 6 is 60 cubic inches greater than the volume of the cylinder with height 10.

(E)The volume of the cylinder with height 6 is 240 / cubic inches greater than the volume of the cylinder with height 10.

Radius of 1 cylinder 6*10 (l*h) is 2pi r1 = 6
Radius of 2 cylinder 10*6 (l*h) is 2pi r2 = 10

Volume of cylinder is pi r square * h

Volume of 1 cylinder = 90/pi
volume of 2 = 150/pi
Difference = 60/pi
_________________

---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------

Please +1 KUDO if my post helps. Thank you.

Intern
Joined: 05 Feb 2014
Posts: 48
Followers: 0

Kudos [?]: 21 [0], given: 49

Re: A 10-by-6 inch piece of paper is used to form the lateral surface of a [#permalink]

### Show Tags

21 Jun 2014, 03:32
Bunuel , can you please explain this problem. I am not able to understand the difference between Option B and D. According to me option D should be correct but its not.
Math Expert
Joined: 02 Sep 2009
Posts: 38297
Followers: 7577

Kudos [?]: 103237 [2] , given: 11369

Re: A 10-by-6 inch piece of paper is used to form the lateral surface of a [#permalink]

### Show Tags

21 Jun 2014, 07:59
2
KUDOS
Expert's post
2
This post was
BOOKMARKED
gauravsoni wrote:
Bunuel , can you please explain this problem. I am not able to understand the difference between Option B and D. According to me option D should be correct but its not.

The difference is that B says "$$\frac{60}{\pi}$$", while D says: "$$60\pi$$". Formatted the original post to make it clearer.

A 10-by-6 inch piece of paper is used to form the lateral surface of a cylinder. If the entire piece of paper is used to make the lateral surface, which of the following must be true of the two possible cylinders that can be formed?

A. The volume of the cylinder with height 10 is $$\frac{60}{\pi}$$ cubic inches greater than the volume of the cylinder with height 6.

B. The volume of the cylinder with height 6 is $$\frac{60}{\pi}$$ cubic inches greater than the volume of the cylinder with height 10.

C. The volume of the cylinder with height 10 is $$60\pi$$ cubic inches greater than the volume of the cylinder with height 6.

D. The volume of the cylinder with height 6 is $$60\pi$$ cubic inches greater than the volume of the cylinder with height 10.

E. The volume of the cylinder with height 6 is $$\frac{240}{\pi}$$ cubic inches greater than the volume of the cylinder with height 10.

We can make 2 cylinders:

With height of 6 and the radius of the base of $$r=\frac{5}{\pi}$$ (from $$2\pi{r}=10$$ --> $$r=\frac{5}{\pi}$$) --> $$volume=\pi{r^2}h=\frac{150}{\pi}$$.

With height of 10 and the radius of the base of $$r=\frac{3}{\pi}$$ (from $$2\pi{r}=6$$ --> $$r=\frac{3}{\pi}$$) --> $$volume=\pi{r^2}h=\frac{90}{\pi}$$.

The volume of the first one is $$\frac{60}{\pi}$$ cubic inches greater than the volume of the second one.

_________________
Intern
Joined: 05 Feb 2014
Posts: 48
Followers: 0

Kudos [?]: 21 [0], given: 49

Re: A 10-by-6 inch piece of paper is used to form the lateral surface of a [#permalink]

### Show Tags

22 Jun 2014, 01:23
Bunuel wrote:
gauravsoni wrote:
Bunuel , can you please explain this problem. I am not able to understand the difference between Option B and D. According to me option D should be correct but its not.

The difference is that B says "$$\frac{60}{\pi}$$", while D says: "$$60\pi$$". Formatted the original post to make it clearer.

A 10-by-6 inch piece of paper is used to form the lateral surface of a cylinder. If the entire piece of paper is used to make the lateral surface, which of the following must be true of the two possible cylinders that can be formed?

A. The volume of the cylinder with height 10 is $$\frac{60}{\pi}$$ cubic inches greater than the volume of the cylinder with height 6.

B. The volume of the cylinder with height 6 is $$\frac{60}{\pi}$$ cubic inches greater than the volume of the cylinder with height 10.

C. The volume of the cylinder with height 10 is $$60\pi$$ cubic inches greater than the volume of the cylinder with height 6.

D. The volume of the cylinder with height 6 is $$60\pi$$ cubic inches greater than the volume of the cylinder with height 10.

E. The volume of the cylinder with height 6 is $$\frac{240}{\pi}$$ cubic inches greater than the volume of the cylinder with height 10.

We can make 2 cylinders:

With height of 6 and the radius of the base of $$r=\frac{5}{\pi}$$ (from $$2\pi{r}=10$$ --> $$r=\frac{5}{\pi}$$) --> $$volume=\pi{r^2}h=\frac{150}{\pi}$$.

With height of 10 and the radius of the base of $$r=\frac{3}{\pi}$$ (from $$2\pi{r}=6$$ --> $$r=\frac{3}{\pi}$$) --> $$volume=\pi{r^2}h=\frac{90}{\pi}$$.

The volume of the first one is $$\frac{60}{\pi}$$ cubic inches greater than the volume of the second one.

Thanks Bunuel, I thought of using the width of the rectangle as the radius, now i see that its actually the circumference of the circular base. Thanks for the clarification.
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15041
Followers: 631

Kudos [?]: 190 [0], given: 0

Re: A 10-by-6 inch piece of paper is used to form the lateral surface of a [#permalink]

### Show Tags

15 Aug 2014, 06:37
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.
_________________
Intern
Joined: 25 Jun 2014
Posts: 48
Followers: 0

Kudos [?]: 21 [0], given: 187

Re: A 10-by-6 inch piece of paper is used to form the lateral surface of a [#permalink]

### Show Tags

21 Sep 2014, 00:03
HI Bunuel,

Can you pls explain how can i know its the circumference of the base? Thank you very much.
Math Expert
Joined: 02 Sep 2009
Posts: 38297
Followers: 7577

Kudos [?]: 103237 [6] , given: 11369

Re: A 10-by-6 inch piece of paper is used to form the lateral surface of a [#permalink]

### Show Tags

21 Sep 2014, 00:22
6
KUDOS
Expert's post
vietnammba wrote:
HI Bunuel,

Can you pls explain how can i know its the circumference of the base? Thank you very much.

When you roll a paper into a cylinder one of the dimensions of the paper becomes the height of the cylinder and the another forms circumference of the base:
Attachments

azn1.1.gif [ 5.23 KiB | Viewed 6678 times ]

_________________
Intern
Joined: 25 Jun 2014
Posts: 48
Followers: 0

Kudos [?]: 21 [0], given: 187

Re: A 10-by-6 inch piece of paper is used to form the lateral surface of a [#permalink]

### Show Tags

21 Sep 2014, 00:30
I get it now, thank you
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15041
Followers: 631

Kudos [?]: 190 [0], given: 0

Re: A 10-by-6 inch piece of paper is used to form the lateral surface of a [#permalink]

### Show Tags

14 Oct 2015, 09:14
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.
_________________
SVP
Joined: 17 Jul 2014
Posts: 2476
Location: United States (IL)
Concentration: Finance, Economics
Schools: Stanford '19 (D)
GMAT 1: 650 Q49 V30
GPA: 3.92
WE: General Management (Transportation)
Followers: 26

Kudos [?]: 316 [0], given: 160

Re: A 10-by-6 inch piece of paper is used to form the lateral surface of a [#permalink]

### Show Tags

08 Jan 2016, 19:31
we have 2 possible cylinders:
h=10, or h=6.
now, with radius, it is more tricky.
We know that Circumference is 2piR.
now, if h=10, then 2piR=6, or R=3/pi
if h=6, then 2piR=10, or 5/pi.

volume is pi*r^2*h.
1. h=10, r=3/pi. volume is 90/pi
2. h=6, r=5/pi. volume is 150/pi.

we can eliminate right away A, C, and E. - A, B because the cylinder with h=6 is greater. E because the difference is 60/pi and not 240/pi.
D is incorrect because it tells 60pi, when actually it is 60/pi.

B thus is the correct answer.
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 15041
Followers: 631

Kudos [?]: 190 [0], given: 0

Re: A 10-by-6 inch piece of paper is used to form the lateral surface of a [#permalink]

### Show Tags

01 Jan 2017, 14:56
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.
_________________
Re: A 10-by-6 inch piece of paper is used to form the lateral surface of a   [#permalink] 01 Jan 2017, 14:56
Similar topics Replies Last post
Similar
Topics:
A four inch by four inch square sheet of paper was folded to form a cy 1 02 Oct 2016, 05:59
4 The surface of a mirror is composed of a rectangular piece that is 9 9 26 Aug 2016, 21:16
A piece of ribbon 4 yards long is used to make bows requiring 15 inche 4 15 Oct 2016, 14:19
3 If the surface area of a cylinder with a radius of 4 inches and a 12 08 Aug 2015, 02:59
6 A manufacturer is using glass as the surface 7 18 Aug 2016, 02:01
Display posts from previous: Sort by