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A rectangular box, with dimensions of 12 inches by 18 inches by 10 inc

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A rectangular box, with dimensions of 12 inches by 18 inches by 10 inc [#permalink]

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New post 17 May 2017, 10:38
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A rectangular box, with dimensions of 12 inches by 18 inches by 10 inches, contains soup cans. If each can is a cylinder with a radius of 3 inches and a height of 5 inches, what is the maximum number of soup cans that the box can contain?

A. 6
B. 12
C. 15
D. 30
E. 48
[Reveal] Spoiler: OA

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Re: A rectangular box, with dimensions of 12 inches by 18 inches by 10 inc [#permalink]

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New post 18 May 2017, 06:38
SajjadAhmad wrote:
A rectangular box, with dimensions of 12 inches by 18 inches by 10 inches, contains soup cans. If each can is a cylinder with a radius of 3 inches and a height of 5 inches, what is the maximum number of soup cans that the box can contain?

A. 6
B. 12
C. 15
D. 30
E. 48



Is the answer C? Please advise.
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Re: A rectangular box, with dimensions of 12 inches by 18 inches by 10 inc [#permalink]

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New post 18 May 2017, 06:44
Michaelkalend13 wrote:
SajjadAhmad wrote:
A rectangular box, with dimensions of 12 inches by 18 inches by 10 inches, contains soup cans. If each can is a cylinder with a radius of 3 inches and a height of 5 inches, what is the maximum number of soup cans that the box can contain?

A. 6
B. 12
C. 15
D. 30
E. 48



Is the answer C? Please advise.


You can check the Official Answer (OA) of a question under the spoiler in the first post. The OA for this question is B.
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Re: A rectangular box, with dimensions of 12 inches by 18 inches by 10 inc [#permalink]

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New post 18 May 2017, 06:47
Bunuel wrote:
Michaelkalend13 wrote:
SajjadAhmad wrote:
A rectangular box, with dimensions of 12 inches by 18 inches by 10 inches, contains soup cans. If each can is a cylinder with a radius of 3 inches and a height of 5 inches, what is the maximum number of soup cans that the box can contain?

A. 6
B. 12
C. 15
D. 30
E. 48



Is the answer C? Please advise.


You can check the Official Answer (OA) of a question under the spoiler in the first post. The OA for this question is B.


Hi Bunuel! Thanks for your prompt response.
Can you please provide an explanation for the answer? Thanks in advance!
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Re: A rectangular box, with dimensions of 12 inches by 18 inches by 10 inc [#permalink]

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New post 18 May 2017, 06:51
18/6=3 cans can be arranged along the length and12/6 = 2 along the breadth.so no of cans arranged in one layer would be 3*2=6
since the height of box is 10, so two layers can be arrangedi.e 6*2=12
Hence answer should be B

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Re: A rectangular box, with dimensions of 12 inches by 18 inches by 10 inc [#permalink]

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New post 18 May 2017, 07:13
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SajjadAhmad wrote:
A rectangular box, with dimensions of 12 inches by 18 inches by 10 inches, contains soup cans. If each can is a cylinder with a radius of 3 inches and a height of 5 inches, what is the maximum number of soup cans that the box can contain?

A. 6
B. 12
C. 15
D. 30
E. 48


The question comes down to determining how to orient the box. Do, we make the HEIGHT of the box 12 inches, 18 inches or 10 inches?
Well, since the height of each CAN is 5 inches, we can see that making the HEIGHT of the box 10 inches is a great course of action. Otherwise, there will be empty space above the cans.

Also, if the radius of each can is 3 inches, then the DIAMETER = 6 inches
So, we want the base of the box to be such that we can fit as many 6-inch diameters into it.
Since 12 inches and 18 inches are both multiples of 6 inches, we can maximize the number of cans by making the 12-inch by 18-inch part of the box the base.

Since with a 12-inch by 18-inch base, we can place 3 rows of 2 cans on the base. This is a total of 6 cans (so far)
Then, we can place a second level of 6 cans on top of the first 6 cans.

So, the most cans we can place in the box = 6 + 6 = 12

Answer:
[Reveal] Spoiler:
B


Cheers,
Brent
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A rectangular box, with dimensions of 12 inches by 18 inches by 10 inc [#permalink]

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New post 18 May 2017, 07:39
SajjadAhmad wrote:
A rectangular box, with dimensions of 12 inches by 18 inches by 10 inches, contains soup cans. If each can is a cylinder with a radius of 3 inches and a height of 5 inches, what is the maximum number of soup cans that the box can contain?

A. 6
B. 12
C. 15
D. 30
E. 48

\(Maximum \ number \ of \ soup \ cans = \frac{Volume \ of \ Rectangular \ Box}{Volume \ of \ Cylinder}\)

\(Maximum \ number \ of \ soup \ cans = \frac{12*18*10}{π*3^2*5}\)

\(Maximum \ number \ of \ soup \ cans = \frac{12*18*10}{22/7*9*5}\)

\(Maximum \ number \ of \ soup \ cans = \frac{12*2*2*7}{22}\)

\(Maximum \ number \ of \ soup \ cans ~ 15.xx\)

Thus, the answer must be (C) 15
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Re: A rectangular box, with dimensions of 12 inches by 18 inches by 10 inc [#permalink]

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New post 18 May 2017, 07:45
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Abhishek009 wrote:
SajjadAhmad wrote:
A rectangular box, with dimensions of 12 inches by 18 inches by 10 inches, contains soup cans. If each can is a cylinder with a radius of 3 inches and a height of 5 inches, what is the maximum number of soup cans that the box can contain?

A. 6
B. 12
C. 15
D. 30
E. 48

\(Maximum \ number \ of \ soup \ cans = \frac{Volume \ of \ Rectangular \ Box}{Volume \ of \ Cylinder}\)

\(Maximum \ number \ of \ soup \ cans = \frac{12*18*10}{π*3^2*5}\)

\(Maximum \ number \ of \ soup \ cans = \frac{12*18*10}{22/7*9*5}\)

\(Maximum \ number \ of \ soup \ cans = \frac{12*2*2*7}{22}\)

\(Maximum \ number \ of \ soup \ cans ~ 15.xx\)

Thus, the answer must be (C) 15


Hi Abhishek009,

This answer would be correct if we could squish the cans into any shape we wish, in which case we need only concern ourselves with the volume of each case.
However, I believe the intent of this question is to keep the same cylindrical shape of each can, in which case there will be some space in the packed box that is just air.

Cheers,
Brent
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Re: A rectangular box, with dimensions of 12 inches by 18 inches by 10 inc   [#permalink] 18 May 2017, 07:45
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A rectangular box, with dimensions of 12 inches by 18 inches by 10 inc

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