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

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Math Expert
Joined: 02 Sep 2009
Posts: 59708
Four identical cylinders are to be packed standing upright in the same  [#permalink]

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18 Sep 2018, 21:50
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95% (hard)

Question Stats:

30% (02:18) correct 70% (02:19) wrong based on 89 sessions

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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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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.

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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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.

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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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).
Math Expert
Joined: 02 Aug 2009
Posts: 8306
Re: Four identical cylinders are to be packed standing upright in the same  [#permalink]

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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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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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Posts: 507
Location: Malaysia
GMAT 1: 700 Q50 V33
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Re: Four identical cylinders are to be packed standing upright in the same  [#permalink]

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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.
Math Expert
Joined: 02 Aug 2009
Posts: 8306
Re: Four identical cylinders are to be packed standing upright in the same  [#permalink]

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