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# The largest possible cylinder is enclosed in a cube. What is the large

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Math Expert
Joined: 02 Sep 2009
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The largest possible cylinder is enclosed in a cube. What is the large  [#permalink]

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17 Sep 2018, 22:16
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45% (medium)

Question Stats:

55% (00:58) correct 45% (00:53) wrong based on 41 sessions

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The largest possible cylinder is enclosed in a cube. What is the largest possible volume of the cylinder?

(1) The volume of the cube is 64 cubic units.
(2) The radius of the cylinder is 2 units.

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Re: The largest possible cylinder is enclosed in a cube. What is the large  [#permalink]

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17 Sep 2018, 23:13
Bunuel wrote:
The largest possible cylinder is enclosed in a cube. What is the largest possible volume of the cylinder?

(1) The volume of the cube is 64 cubic units.
(2) The radius of the cylinder is 2 units.

IMO A

Statement 1: The volume of the cube is 64 cubic units:
This will restrict the height of the cylinder and radius of its base, so maximum possible volume can be determined.
SUFFICIENT

Statement 2: The radius of the cylinder is 2 units
This does not restrict the height of the cylinder, so the volume could be anything.
INSUFFICIENT
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Re: The largest possible cylinder is enclosed in a cube. What is the large  [#permalink]

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18 Sep 2018, 00:30
GMATisLovE wrote:
Bunuel wrote:
The largest possible cylinder is enclosed in a cube. What is the largest possible volume of the cylinder?

(1) The volume of the cube is 64 cubic units.
(2) The radius of the cylinder is 2 units.

IMO A

Statement 1: The volume of the cube is 64 cubic units:
This will restrict the height of the cylinder and radius of its base, so maximum possible volume can be determined.
SUFFICIENT

Statement 2: The radius of the cylinder is 2 units
This does not restrict the height of the cylinder, so the volume could be anything.
INSUFFICIENT

Hi,

The question mentions that the cylinder that's been enclosed is the largest possible. I guess that would mean that the cylinder has diameter of the same length as one of its sides. From statement 2, we know that the radius is 2 and thus, diameter is 4. Again, largest possible would imply that the height would be equal to the side of the cube which makes this statement sufficient in my opinion. What do you think?
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Re: The largest possible cylinder is enclosed in a cube. What is the large  [#permalink]

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18 Sep 2018, 13:21
Shruti0805 wrote:
GMATisLovE wrote:
Bunuel wrote:
The largest possible cylinder is enclosed in a cube. What is the largest possible volume of the cylinder?

(1) The volume of the cube is 64 cubic units.
(2) The radius of the cylinder is 2 units.

IMO A

Statement 1: The volume of the cube is 64 cubic units:
This will restrict the height of the cylinder and radius of its base, so maximum possible volume can be determined.
SUFFICIENT

Statement 2: The radius of the cylinder is 2 units
This does not restrict the height of the cylinder, so the volume could be anything.
INSUFFICIENT

Hi,

The question mentions that the cylinder that's been enclosed is the largest possible. I guess that would mean that the cylinder has diameter of the same length as one of its sides. From statement 2, we know that the radius is 2 and thus, diameter is 4. Again, largest possible would imply that the height would be equal to the side of the cube which makes this statement sufficient in my opinion. What do you think?

Hi Shruti,

Yes, I think you are right. I missed the point you mentioned.
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Re: The largest possible cylinder is enclosed in a cube. What is the large  [#permalink]

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18 Sep 2018, 16:49
Experts can you please provide a solution to this question?

Bunuel chetan2u
Math Expert
Joined: 02 Aug 2009
Posts: 7763
Re: The largest possible cylinder is enclosed in a cube. What is the large  [#permalink]

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18 Sep 2018, 18:13
2
The largest possible cylinder is enclosed in a cube. What is the largest possible volume of the cylinder?

(1) The volume of the cube is 64 cubic units.
Largest possible cylinder will be that will be fit JUST exactly into the cube...
So cubes dimensions are 4*4*4, height of cylinder=2 and diameter also is 4..
Thus volume = $$\pi*2^2*4=16\pi$$
Sufficient

(2) The radius of the cylinder is 2 units.
We are given that the cylinder is fitted in cube, so if radius is 2 the diameter will be 4 ..
And the diameter will also be equal to the side of cube...
Since all dimensions of a cube are same, the diameter of cylinder will be SAME as the height..
Thus volume = $$\pi*2^2*4=16\pi$$
Sufficient

D
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Re: The largest possible cylinder is enclosed in a cube. What is the large  [#permalink]

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18 Sep 2018, 21:12
Why are we not considering cylinder formed along the diagonal of the cube?? Will it not be largest possible??

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Re: The largest possible cylinder is enclosed in a cube. What is the large   [#permalink] 18 Sep 2018, 21:12
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