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

Question

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

A)  \frac{60}{π}

B)  \frac{90}{π}

C)  \frac{150}{π}

D) 360π

E) 600π

chetan2u · Accepted Answer

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

TurgCorp · Answer

You are correct. That phrasing was adjusted. Thank you!

FacelessMan · Answer

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.

sauravpaul · Answer

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

GloryBoy92 · Answer

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?

jfranciscocuencag · Answer

I have the same question as  GloryBoy92

Can someone please explain to us?

Kind regads!

dine5207 · Answer

Fdambro294 · Answer

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) *  '2 * 6
 = (pi) *   * 6 (don't forget to ALSO Square the DEN = pi)
 
 Answer = 150 / (pi)

Sabby · Answer

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!

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

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