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

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TurgCorp
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A thin rectangular sheet of metal is 6 inches wide and 10 inches long [#permalink] 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
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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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chetan2u
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Re: A thin rectangular sheet of metal is 6 inches wide and 10 inches long [#permalink] 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 \(\frac{150}{pi}\)
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TurgCorp
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Re: A thin rectangular sheet of metal is 6 inches wide and 10 inches long [#permalink] New post  15 May 2016, 00:07
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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] New post  01 Jun 2016, 15:00
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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] New post  01 Jun 2016, 20:23
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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] New post  11 Jun 2019, 11:38
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 largest possible cylinder?


A) \(\frac{60}{π}\)

B) \(\frac{90}{π}\)

C) \(\frac{150}{π}\)

D) 360π

E) 600π


Hi guys,

I knew that the radius had to be the highest because it gets squared

Here's my answer

Volume of cylinder = π * R^2 * Height
= π * 5^2 * 6
= π * 150

Why is the answer 150/π instead of π150?

What am i doing wrong?
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jfranciscocuencag
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Re: A thin rectangular sheet of metal is 6 inches wide and 10 inches long [#permalink] New post  17 Jun 2019, 16:27
GloryBoy92 wrote:
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 largest possible cylinder?


A) \(\frac{60}{π}\)

B) \(\frac{90}{π}\)

C) \(\frac{150}{π}\)

D) 360π

E) 600π


Hi guys,

I knew that the radius had to be the highest because it gets squared

Here's my answer

Volume of cylinder = π * R^2 * Height
= π * 5^2 * 6
= π * 150

Why is the answer 150/π instead of π150?

What am i doing wrong?


I have the same question as GloryBoy92

Can someone please explain to us?

Kind regads!
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dine5207
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Re: A thin rectangular sheet of metal is 6 inches wide and 10 inches long [#permalink] New post  25 Jul 2020, 06:26
GloryBoy92 wrote:
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 largest possible cylinder?


A) \(\frac{60}{π}\)

B) \(\frac{90}{π}\)

C) \(\frac{150}{π}\)

D) 360π

E) 600π


Hi guys,

I knew that the radius had to be the highest because it gets squared

Here's my answer

Volume of cylinder = π * R^2 * Height
= π * 5^2 * 6 {If you read question clearly it says circumference of a circle,which means 2*Pi*r=10 }
= π * 150

Why is the answer 150/π instead of π150?

What am i doing wrong?
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Fdambro294
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A thin rectangular sheet of metal is 6 inches wide and 10 inches long [#permalink] New post  10 Aug 2020, 22:58
if the Circumference = 2 * pi * r = 10

then the radius = r = 5 / (pi) and height of cylinder = 6

Volume of Cylinder = (pi) * r'2 * h

= (pi) * [ 5 / (pi) ]'2 * 6
= (pi) * [ 25 / (pi)'2 ] * 6 (don't forget to ALSO Square the DEN = pi)

Answer = 150 / (pi) [ (pi) in the NUM Cancels with (pi) in the DEN ]
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Re: A thin rectangular sheet of metal is 6 inches wide and 10 inches long [#permalink] New post  20 Mar 2021, 11:50
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Hi,

I just came across this question, my answer might be a bit late but it could help other people. I had the same concern about 150n. (note n=pi)

In order to maximize the volume we'll maximize the radius therefore taking the longest side of the rectangle as the circumference.

Circumference = 10 = 2r*n
r*n=10/2=5
r=5/n

In your question below, you wrote r=5 instead of r=5/n

Now that we have our radius, let's calculate the volume :
V= r^2*n*h
V=(5/n)^2*n*6
V=(25/n^2) *n *6
V= 25/n*6 = 150/n

Answer C!

jfranciscocuencag wrote:
GloryBoy92 wrote:
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 largest possible cylinder?


A) \(\frac{60}{π}\)

B) \(\frac{90}{π}\)

C) \(\frac{150}{π}\)

D) 360π

E) 600π


Hi guys,

I knew that the radius had to be the highest because it gets squared

Here's my answer

Volume of cylinder = π * R^2 * Height
= π * 5^2 * 6
= π * 150

Why is the answer 150/π instead of π150?

What am i doing wrong?


I have the same question as GloryBoy92

Can someone please explain to us?

Kind regads!
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Re: A thin rectangular sheet of metal is 6 inches wide and 10 inches long [#permalink] New post  26 Sep 2023, 07:32
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