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Four identical cylinders are to be packed standing upright in the same

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Four identical cylinders are to be packed standing upright in the same  [#permalink]

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New post 18 Sep 2018, 21:50
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Four identical cylinders are to be packed standing upright in the same direction into a rectangular shipping box with dimensions 3 x 12 x 4. What is the maximum possible volume of one of the cylinders?


A. 48π
B. 27π
C. 12π
D. 9π
E. 6.75π

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Re: Four identical cylinders are to be packed standing upright in the same  [#permalink]

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New post 19 Sep 2018, 01:29
1
Bunuel wrote:
Four identical cylinders are to be packed standing upright in the same direction into a rectangular shipping box with dimensions 3 x 12 x 4. What is the maximum possible volume of one of the cylinders?


A. 48π
B. 27π
C. 12π
D. 9π
E. 6.75π


As we're asked for the maximal possible value, we'll look at the extremes.
This is a Logical approach.

We are told that width = 3, length = 12 and height = 4.
Then the diameter of the circle is at most 3 and the height at most 4.
This gives a total volume of (1.5)^2 * 4 * pi = 9pi per cylinder.

(D) is our answer.

Instead of figuring out all the different arrangements, we'll first try estimating.
This is an Alternative approach.

Note that we could also have guessed that this is the answer rather easily (an Alternative approach):
Dividing the box into 4 equal parts of 3*3*4 gives a total volume of 36 for the box enclosing the cylinder.
Since (A), (B), (C) are all larger than this, they are eliminated.
Even without calculating, we can eyeball that (E) looks way too small and so (D) is a much better bet.
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Re: Four identical cylinders are to be packed standing upright in the same  [#permalink]

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New post 06 Oct 2018, 06:44
DavidTutorexamPAL wrote:
Bunuel wrote:
Four identical cylinders are to be packed standing upright in the same direction into a rectangular shipping box with dimensions 3 x 12 x 4. What is the maximum possible volume of one of the cylinders?


A. 48π
B. 27π
C. 12π
D. 9π
E. 6.75π


As we're asked for the maximal possible value, we'll look at the extremes.
This is a Logical approach.

We are told that width = 3, length = 12 and height = 4.
Then the diameter of the circle is at most 3 and the height at most 4.
This gives a total volume of (1.5)^2 * 4 * pi = 9pi per cylinder.

(D) is our answer.

Instead of figuring out all the different arrangements, we'll first try estimating.
This is an Alternative approach.

Note that we could also have guessed that this is the answer rather easily (an Alternative approach):
Dividing the box into 4 equal parts of 3*3*4 gives a total volume of 36 for the box enclosing the cylinder.
Since (A), (B), (C) are all larger than this, they are eliminated.
Even without calculating, we can eyeball that (E) looks way too small and so (D) is a much better bet.


the quest is asking `volume of ONE of the cylinders` not total of 4, isnt it?
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Four identical cylinders are to be packed standing upright in the same  [#permalink]

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New post 06 Oct 2018, 23:42
Bunuel wrote:
Four identical cylinders are to be packed standing upright in the same direction into a rectangular shipping box with dimensions 3 x 12 x 4. What is the maximum possible volume of one of the cylinders?


A. 48π
B. 27π
C. 12π
D. 9π
E. 6.75π


Hi Bunuel, chetan2u,

When in a question its mentioned that the dimension is x*y*z, should we always consider it as - l*b*h (i.e. length =x, breadth = y,height = z).
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Re: Four identical cylinders are to be packed standing upright in the same  [#permalink]

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New post 07 Oct 2018, 00:02
1
rahul16singh28 wrote:
Bunuel wrote:
Four identical cylinders are to be packed standing upright in the same direction into a rectangular shipping box with dimensions 3 x 12 x 4. What is the maximum possible volume of one of the cylinders?


A. 48π
B. 27π
C. 12π
D. 9π
E. 6.75π


Hi Bunuel, chetan2u,

When in a question its mentioned that the dimension is x*y*z, should we always consider it as - l*b*h (i.e. length =x, breadth = y,height = z).


rahul16singh28
I would take sides as any dimensions and would work for maximum possible volume.
Max possible volume is when the entire box is completely filled...
Now four cylinder and 4*3=12
So if I place all four in the base in a straight line and have dimensions 3*12 of base..
I can get four placed one by one and entire height of 4 becomes the height of cylinder.
As cylinder's volume is πr^2h, we have to maximize radius.

But above method we get max radius as 3/2=1.5
So volume = π*(1.5)^2*4=9π
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Re: Four identical cylinders are to be packed standing upright in the same  [#permalink]

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New post 07 Oct 2018, 20:42
So chetan2u

How did you take 4×3?

My approach was also the same.. to maximize pi*r^2*h..
We have to max out r but couldn't get any further

Posted from my mobile device
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Re: Four identical cylinders are to be packed standing upright in the same  [#permalink]

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New post 07 Oct 2018, 20:59
saurabh9gupta wrote:
So chetan2u

How did you take 4×3?

My approach was also the same.. to maximize pi*r^2*h..
We have to max out r but couldn't get any further

Posted from my mobile device


Hi saurabh9gupta

The only way to adjust 4 Cylinders in the Shipping Box is when the Breadth of the Box = 12 and each cylinder diameter will be 3.

Hope it clarifies.
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Re: Four identical cylinders are to be packed standing upright in the same  [#permalink]

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New post 07 Oct 2018, 21:35
saurabh9gupta wrote:
So chetan2u

How did you take 4×3?

My approach was also the same.. to maximize pi*r^2*h..
We have to max out r but couldn't get any further

Posted from my mobile device


Hi..

We take base as 12*3 so dia of each cylinder is 3 and along the length of 12, we can fit 4 cylinders that makes it 4*3=12
In this arrangement, we use every possible region in the cylinder..
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3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html


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Re: Four identical cylinders are to be packed standing upright in the same &nbs [#permalink] 07 Oct 2018, 21:35
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