Find all School-related info fast with the new School-Specific MBA Forum

 It is currently 25 Aug 2016, 06:12

### 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

Author Message
TAGS:

### Hide Tags

Senior Manager
Joined: 28 Aug 2010
Posts: 256
Followers: 6

Kudos [?]: 440 [1] , given: 11

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

### Show Tags

10 Jan 2011, 19:00
1
KUDOS
5
This post was
BOOKMARKED
00:00

Difficulty:

55% (hard)

Question Stats:

57% (02:28) correct 43% (01:12) wrong based on 256 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 21 Jun 2014, 07:43, edited 1 time in total.
Edited the question
Intern
Joined: 08 Jun 2010
Posts: 10
Followers: 0

Kudos [?]: 2 [0], given: 1

Re: A 10-by-6 inch piece of paper is used to form [#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
Joined: 05 Feb 2014
Posts: 48
Followers: 0

Kudos [?]: 13 [0], given: 49

Re: A 10-by-6 inch piece of paper is used to form [#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: 34432
Followers: 6255

Kudos [?]: 79448 [2] , given: 10016

Re: A 10-by-6 inch piece of paper is used to form [#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 [?]: 13 [0], given: 49

Re: A 10-by-6 inch piece of paper is used to form [#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.
Intern
Joined: 25 Jun 2014
Posts: 48
Followers: 0

Kudos [?]: 19 [0], given: 187

Re: A 10-by-6 inch piece of paper is used to form [#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: 34432
Followers: 6255

Kudos [?]: 79448 [4] , given: 10016

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

### Show Tags

21 Sep 2014, 00:22
4
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 4935 times ]

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

Kudos [?]: 19 [0], given: 187

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

### Show Tags

21 Sep 2014, 00:30
I get it now, thank you
GMAT Club Legend
Joined: 09 Sep 2013
Posts: 11050
Followers: 510

Kudos [?]: 134 [0], given: 0

Re: A 10-by-6 inch piece of paper is used to form [#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: 1636
Location: United States
Schools: Stanford '19
GMAT 1: 550 Q39 V27
GMAT 2: 560 Q42 V26
GMAT 3: 560 Q43 V24
GMAT 4: 650 Q49 V30
GPA: 3.56
WE: General Management (Transportation)
Followers: 12

Kudos [?]: 193 [0], given: 109

Re: A 10-by-6 inch piece of paper is used to form [#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.
Re: A 10-by-6 inch piece of paper is used to form   [#permalink] 08 Jan 2016, 19:31
Similar topics Replies Last post
Similar
Topics:
1 A picture is copied onto a sheet of paper 8.5 inches by 10 inches. A 1 2 14 May 2016, 14:12
A piece of ribbon 4 yards long is used to make bows requiring 15 inche 2 14 May 2016, 14:09
6 A sheet of paper ABDE is a 12-by-18-inch rectangle, as shown in Figure 3 04 May 2015, 06:09
3 A semicircular piece of paper has center O, as shown above. Its diamet 5 04 May 2015, 05:45
4 A 10-by-6 inch piece of paper is used to form the lateral 10 28 Jul 2011, 09:34
Display posts from previous: Sort by