Jul 19 08:00 AM PDT  09:00 AM PDT The Competition Continues  Game of Timers is a teambased competition based on solving GMAT questions to win epic prizes! Starting July 1st, compete to win prep materials while studying for GMAT! Registration is Open! Ends July 26th Jul 20 07:00 AM PDT  09:00 AM PDT Attend this webinar and master GMAT SC in 10 days by learning how meaning and logic can help you tackle 700+ level SC questions with ease. Jul 21 07:00 AM PDT  09:00 AM PDT Attend this webinar to learn a structured approach to solve 700+ Number Properties question in less than 2 minutes
Author 
Message 
TAGS:

Hide Tags

Manager
Joined: 28 Aug 2010
Posts: 169

A 10by6 inch piece of paper is used to form the lateral surface of a
[#permalink]
Show Tags
Updated on: 02 Jan 2017, 04:55
Question Stats:
63% (02:24) correct 37% (02:37) wrong based on 272 sessions
HideShow timer Statistics
A 10by6 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.
Official Answer and Stats are available only to registered users. Register/ Login.
Originally posted by ajit257 on 10 Jan 2011, 19:00.
Last edited by Bunuel on 02 Jan 2017, 04:55, edited 2 times in total.
Edited the question




Math Expert
Joined: 02 Sep 2009
Posts: 56261

Re: A 10by6 inch piece of paper is used to form the lateral surface of a
[#permalink]
Show Tags
21 Sep 2014, 00:22
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 13400 times ]
_________________




Intern
Joined: 18 Jul 2011
Posts: 43

Re: A 10by6 inch piece of paper is used to form the lateral surface of a
[#permalink]
Show Tags
28 Jul 2011, 13:05
baker2145 wrote: Here's the question:
A 10by6 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(rsquared)(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: \(2pi(r) = 10\) \(r = \frac{5}{(pi)}\) \(V = (pi)(\frac{5}{pi})^2(6)\) \(V = \frac{150}{pi}\) 15090 = 60 So, B.




Intern
Joined: 08 Jun 2010
Posts: 9

Re: A 10by6 inch piece of paper is used to form the lateral surface of a
[#permalink]
Show Tags
10 Jan 2011, 20:11
Simple math 1. Answer choices asking about difference in volumes 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)



Senior Manager
Joined: 30 Aug 2009
Posts: 260
Location: India
Concentration: General Management

Re: A 10by6 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 10by6 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(rsquared)(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: 38

Re: A 10by6 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)



Manager
Status: Post application wait begins!
Joined: 15 Aug 2010
Posts: 139
Location: United States (CA)
Concentration: Strategy, Technology
GPA: 3.82
WE: Engineering (Computer Software)

Re: A 10by6 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: 117

Re: A 10by6 inch piece of paper is used to form the lateral surface of a
[#permalink]
Show Tags
28 Feb 2013, 13:24
mun23 wrote: A 10by6 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: 42

Re: A 10by6 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: 56261

Re: A 10by6 inch piece of paper is used to form the lateral surface of a
[#permalink]
Show Tags
21 Jun 2014, 07:59
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 10by6 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. Answer: B.
_________________



Intern
Joined: 05 Feb 2014
Posts: 42

Re: A 10by6 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 10by6 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. Answer: B. 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: 36

Re: A 10by6 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.



Intern
Joined: 25 Jun 2014
Posts: 36

Re: A 10by6 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



Board of Directors
Joined: 17 Jul 2014
Posts: 2539
Location: United States (IL)
Concentration: Finance, Economics
GPA: 3.92
WE: General Management (Transportation)

Re: A 10by6 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.
_________________



Manager
Joined: 23 Dec 2013
Posts: 142
Location: United States (CA)
GMAT 1: 710 Q45 V41 GMAT 2: 760 Q49 V44
GPA: 3.76

Re: A 10by6 inch piece of paper is used to form the lateral surface of a
[#permalink]
Show Tags
22 May 2017, 19:16
ajit257 wrote: A 10by6 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. The trick of this problem is to realize that 6in or 10in, the given length and width, are not the radius of the folded piece of paper; they are the circumference. So you need to solve for the circumference of each (5/pi and 3/pi, respectively). Then you plug them into the volume formula (piR^2H) to arrive at 150/pi  90/pi.



Intern
Joined: 16 Oct 2017
Posts: 37

A 10by6 inch piece of paper is used to form the lateral surface of a
[#permalink]
Show Tags
Updated on: 11 Nov 2017, 08:09
V = pi(5/pi)^2 x 6 = 150/pi. I'm confused as too why two pi turns into 150/pi.
V = pi(3/pi)^2 x 10 = 90/pi. I'm confused as too why two pi turns into 90/pi.
Can someone explain? Aren't we supposed to crosscancel the pi out?
Originally posted by OCDianaOC on 10 Nov 2017, 19:25.
Last edited by OCDianaOC on 11 Nov 2017, 08:09, edited 1 time in total.



Math Expert
Joined: 02 Sep 2009
Posts: 56261

Re: A 10by6 inch piece of paper is used to form the lateral surface of a
[#permalink]
Show Tags
11 Nov 2017, 01:37
OCDianaOC wrote: V = pi(5/pi)*2 x 6 = 150/pi. I'm confused as too why two pi turns into 150/pi.
V = pi(3/pi)*2 x 10 = 90/pi. I'm confused as too why two pi turns into 90/pi.
Can someone explain? Aren't we supposed to crosscancel the pi out? The volume formula is \(volume=\pi{r^2}h\). Notice that r there is squared not multiplied by 2.
_________________



Intern
Joined: 16 Oct 2017
Posts: 37

Re: A 10by6 inch piece of paper is used to form the lateral surface of a
[#permalink]
Show Tags
11 Nov 2017, 08:08
Bunuel wrote: OCDianaOC wrote: V = pi(5/pi)*2 x 6 = 150/pi. I'm confused as too why two pi turns into 150/pi.
V = pi(3/pi)*2 x 10 = 90/pi. I'm confused as too why two pi turns into 90/pi.
Can someone explain? Aren't we supposed to crosscancel the pi out? The volume formula is \(volume=\pi{r^2}h\). Notice that r there is squared not multiplied by 2. I'm aware of that. Sorry, I put "*" hoping to imply it meant squared since I couldn't find another symbol for that on my keyboard. Let me rephrase, V = pi(5/pi)^2 x 6 = 150/pi. I'm confused as too why two pi turns into 150/pi. V = pi(3/pi)^2 x 10 = 90/pi. I'm confused as too why two pi turns into 90/pi. Can someone explain? Aren't we supposed to crosscancel the pi out?



Math Expert
Joined: 02 Sep 2009
Posts: 56261

Re: A 10by6 inch piece of paper is used to form the lateral surface of a
[#permalink]
Show Tags
11 Nov 2017, 08:15
OCDianaOC wrote: Bunuel wrote: OCDianaOC wrote: V = pi(5/pi)*2 x 6 = 150/pi. I'm confused as too why two pi turns into 150/pi.
V = pi(3/pi)*2 x 10 = 90/pi. I'm confused as too why two pi turns into 90/pi.
Can someone explain? Aren't we supposed to crosscancel the pi out? The volume formula is \(volume=\pi{r^2}h\). Notice that r there is squared not multiplied by 2. I'm aware of that. Sorry, I put "*" hoping to imply it meant squared since I couldn't find another symbol for that on my keyboard. Let me rephrase, V = pi(5/pi)^2 x 6 = 150/pi. I'm confused as too why two pi turns into 150/pi. V = pi(3/pi)^2 x 10 = 90/pi. I'm confused as too why two pi turns into 90/pi. Can someone explain? Aren't we supposed to crosscancel the pi out? \(\pi\) there is also gets squared. h = 6 and \(r=\frac{5}{\pi}\): \(volume=\pi{r^2}h=\pi*(\frac{5}{\pi})^2*6=\pi*\frac{25}{\pi^2}*6=\frac{150}{\pi}\).
_________________



Intern
Joined: 16 Oct 2017
Posts: 37

Re: A 10by6 inch piece of paper is used to form the lateral surface of a
[#permalink]
Show Tags
11 Nov 2017, 09:12
Oh! That's what I was missing! Thanks Brunel... so we multiple out straight across (squaring num and denom) then cancel out the extra pi from numerator and denominator!




Re: A 10by6 inch piece of paper is used to form the lateral surface of a
[#permalink]
11 Nov 2017, 09:12



Go to page
1 2
Next
[ 22 posts ]



