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

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

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New post Updated on: 16 Sep 2018, 02:11
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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.
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Re: A thin rectangular sheet of metal is 6 inches wide and 10 inches long  [#permalink]

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New post 15 May 2016, 00:02
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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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Re: A thin rectangular sheet of metal is 6 inches wide and 10 inches long  [#permalink]

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New post 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!
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Re: A thin rectangular sheet of metal is 6 inches wide and 10 inches long  [#permalink]

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New post 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.
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Re: A thin rectangular sheet of metal is 6 inches wide and 10 inches long  [#permalink]

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New post 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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New post 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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