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# A thin rectangular sheet of metal is 6 inches wide and 10 inches long

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Intern
Joined: 15 Mar 2015
Posts: 12
Concentration: Operations, Strategy
GMAT 1: 550 Q35 V30
WE: Operations (Manufacturing)
A thin rectangular sheet of metal is 6 inches wide and 10 inches long  [#permalink]

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Updated on: 16 Sep 2018, 02:11
3
7
00:00

Difficulty:

45% (medium)

Question Stats:

68% (02:04) correct 32% (01:41) wrong based on 230 sessions

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A thin rectangular sheet of metal is 6 inches wide and 10 inches long. The sheet of metal is to be rolled into to form a cylinder so that one dimension becomes the circumference of the cylinder and the other dimension becomes the height. What is the volume of the largest possible cylinder?

A) $$\frac{60}{π}$$

B) $$\frac{90}{π}$$

C) $$\frac{150}{π}$$

D) 360π

E) 600π

Originally posted by TurgCorp on 14 May 2016, 23:40.
Last edited by Bunuel on 16 Sep 2018, 02:11, edited 3 times in total.
Math Expert
Joined: 02 Aug 2009
Posts: 7037
Re: A thin rectangular sheet of metal is 6 inches wide and 10 inches long  [#permalink]

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15 May 2016, 00:02
2
TurgCorp wrote:
A thin rectangular sheet of metal is 6 inches wide and 10 inches long. The sheet of metal is to be rolled into to form a cylinder so that one dimension becomes the circumference of the cylinder and the other dimension becomes the height. What is the volume of the cylinder?

A) $$\frac{60}{π}$$
B) $$\frac{90}{π}$$
C) $$\frac{150}{π}$$
D) 360π
E) 600π

Hi,
you are missing on word MAXIMUM volume, as there can be two volumes possible..

Basically one side will become circumference and other height...

1) let 6 as 2 pi *r ..... so $$2pi*r = 6.......... r=\frac{3}{pi}.....$$
so volume = $$pi*r^2h= pi*(\frac{3}{pi})^2*10 = \frac{90}{pi}$$..

2) let 10 be circumference...so $$2pi*r = 10.......... r=\frac{5}{pi}.....$$
so volume =$$pi*r^2h= pi*(\frac{5}{pi})^2*6 = \frac{150}{pi}$$..

greater of two is $$\frac{150}{pi}$$
C
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Intern
Joined: 15 Mar 2015
Posts: 12
Concentration: Operations, Strategy
GMAT 1: 550 Q35 V30
WE: Operations (Manufacturing)
Re: A thin rectangular sheet of metal is 6 inches wide and 10 inches long  [#permalink]

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15 May 2016, 00:07
chetan2u wrote:
Hi,
you are missing on word MAXIMUM volume, as there can be two volumes possible..

You are correct. That phrasing was adjusted. Thank you!
Manager
Joined: 19 Dec 2015
Posts: 111
Location: United States
GMAT 1: 720 Q50 V38
GPA: 3.8
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Re: A thin rectangular sheet of metal is 6 inches wide and 10 inches long  [#permalink]

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01 Jun 2016, 15:00
Instead of calculating 2 vols separately and comparing, this is how I approached this problem :

Volume of the cylinder V = πr^2h, where r=radius of the cylinder and h= height of the cylinder.

Since r has a power of 2, we should focus on increasing the value of r. And in that case, we should fold on the longer side (length = 10)

V = 150/π. Hence C.
Intern
Joined: 01 May 2015
Posts: 41
Re: A thin rectangular sheet of metal is 6 inches wide and 10 inches long  [#permalink]

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01 Jun 2016, 20:23
Volume = pi*r^2*h

Since we have r^2, clearly r should be maximum.

"r" will be maximum, when 10 inches is the circumference.
=> 2*pi*r = 10
=> r = 5/pi

So, volume = pi*r^2*h = pi*(5/pi)^2*6 = 150/pi
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Re: A thin rectangular sheet of metal is 6 inches wide and 10 inches long  [#permalink]

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16 Sep 2018, 01:59
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Re: A thin rectangular sheet of metal is 6 inches wide and 10 inches long &nbs [#permalink] 16 Sep 2018, 01:59
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