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A certain rectangular crate measures 8 feet by 10 feet by 12

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A certain rectangular crate measures 8 feet by 10 feet by 12 [#permalink]

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New post 01 Sep 2010, 11:20
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A certain rectangular crate measures 8 feet by 10 feet by 12 feet. A cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its six faces. What should the radius of the tank be if it is to be of the largest possible volume?

A. 4
B. 5
C. 6
D. 8
E. 10
[Reveal] Spoiler: OA

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Re: Problem Solving [#permalink]

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New post 01 Sep 2010, 12:14
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aiming4mba wrote:
A certain rectangular crate measures 8 feet by 10 feet by 12 feet. A cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its six faces. What should the radius of the tank be if it is to be of the largest possible volume?

a. 4
b. 5
c. 6
d. 8
e. 10


Volume of the cylinder equals to \(area=\pi{r^2}h\). First of all note that answer choices C, D, and E don't make sense. For example cylinder of a radius 6 (option C) just won't fit on any face, as max face has a dimensions 12*10 so cylinder with max radius of 5 can be placed on it.

Max volume will be when the base of a cylinder is placed on the face with dimension 12*10 thus the radius will be 5 --> \(v=\pi{5^2}*8=200\pi\);

Other options:
If we place cylinder on the face with dimension 12*8 then radius will be 4 and \(v=\pi{4^2}*10=160\pi\);
If we place cylinder on the face with dimension 10*8 then radius will be 4 and \(v=\pi{4^2}*12=192\pi\),.

Answer: B.
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Re: Problem Solving [#permalink]

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New post 01 Sep 2010, 23:21
Good explaination

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Re: A certain rectangular crate measures 8 feet by 10 feet by 12 [#permalink]

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New post 31 Aug 2013, 15:55
Bunuel wrote:
Bumping for review and further discussion.


I don't agree with the solution, the radius can be 6. Also if you consider it will less than 6, it will be more of about 5.9 which is closer to 6 than 5. So i will mark 6 in this case.

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Re: A certain rectangular crate measures 8 feet by 10 feet by 12 [#permalink]

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New post 31 Aug 2013, 15:58
Bluelagoon wrote:
Bunuel wrote:
Bumping for review and further discussion.


I don't agree with the solution, the radius can be 6. Also if you consider it will less than 6, it will be more of about 5.9 which is closer to 6 than 5. So i will mark 6 in this case.


The radius cannot be 6. It won't fit on any face.
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Re: A certain rectangular crate measures 8 feet by 10 feet by 12 [#permalink]

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New post 31 Aug 2013, 16:16
Bunuel wrote:
Bluelagoon wrote:
Bunuel wrote:
Bumping for review and further discussion.


I don't agree with the solution, the radius can be 6. Also if you consider it will less than 6, it will be more of about 5.9 which is closer to 6 than 5. So i will mark 6 in this case.


The radius cannot be 6. It won't fit on any face.


12x10. its close enough to have the radius as 6.

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Re: A certain rectangular crate measures 8 feet by 10 feet by 12 [#permalink]

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New post 31 Aug 2013, 16:18
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Bluelagoon wrote:
Bunuel wrote:
Bluelagoon wrote:
I don't agree with the solution, the radius can be 6. Also if you consider it will less than 6, it will be more of about 5.9 which is closer to 6 than 5. So i will mark 6 in this case.


The radius cannot be 6. It won't fit on any face.


12x10. its close enough to have the radius as 6.


The radius of 6 means that the diameter is 12. So, the base of the cylinder will be 12 by 12 and it won't fit.
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Re: A certain rectangular crate measures 8 feet by 10 feet by 12 [#permalink]

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New post 31 Aug 2013, 16:40
yaa. I see .Good question. Thanks!

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Re: A certain rectangular crate measures 8 feet by 10 feet by 12 [#permalink]

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New post 27 Sep 2015, 01:23
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A certain rectangular crate measures 8 feet by 10 feet by 12 [#permalink]

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New post 17 Jul 2016, 03:32
aiming4mba wrote:
A certain rectangular crate measures 8 feet by 10 feet by 12 feet. A cylindrical gas tank is to be made for shipment in the crate and will stand upright when the crate is placed on one of its six faces. What should the radius of the tank be if it is to be of the largest possible volume?

A. 4
B. 5
C. 6
D. 8
E. 10


Make the base of the crate as 10 feet by 12 feet
The biggest object that can fit in this base is 10 feet by 10 feet; If we take an object with dimension of 11 feet then it will pop 1 feet out out that side of the base that is 10 feet.
Therefore the biggest cylinder has to have a diameter of 10 and not more than that
Radius will be half of diameter= 10/2 = 5
5 feet is the answer
So the corect option is B
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Re: A certain rectangular crate measures 8 feet by 10 feet by 12 [#permalink]

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New post 23 Aug 2017, 06:54
Hello from the GMAT Club BumpBot!

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Re: A certain rectangular crate measures 8 feet by 10 feet by 12   [#permalink] 23 Aug 2017, 06:54
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