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# The largest possible cube is enclosed in a cylinder and has volume 64.

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Math Expert
Joined: 02 Sep 2009
Posts: 58118
The largest possible cube is enclosed in a cylinder and has volume 64.  [#permalink]

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17 Sep 2018, 21:59
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Difficulty:

55% (hard)

Question Stats:

55% (01:42) correct 45% (01:23) wrong based on 37 sessions

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The largest possible cube is enclosed in a cylinder and has volume 64. What is the volume of the cylinder if its height is 12?

A. 384π
B. 192π
C. 144π
D. 96π
E. 48π

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Re: The largest possible cube is enclosed in a cylinder and has volume 64.  [#permalink]

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19 Sep 2018, 01:16
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Bunuel wrote:
The largest possible cube is enclosed in a cylinder and has volume 64. What is the volume of the cylinder if its height is 12?

A. 384π
B. 192π
C. 144π
D. 96π
E. 48π

The volume of a sphere is given by Side^3 = 64
So Side = 4

When a largest possible cube is enclosed in a cylinder, the diagonal of the bottom face of the cube will be the diameter of the cylinder.
Diagonal of the bottom face = $$4*\sqrt{2}$$

So radius of the cylinder = $$(4*\sqrt{2})/2 = 2\sqrt{2}$$

Volume of the cylinder = $$\pi*r^2 * h = \pi * (2\sqrt{2})^2 * 12 = 96\pi$$
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Re: The largest possible cube is enclosed in a cylinder and has volume 64.  [#permalink]

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17 Sep 2018, 22:07
Bunuel wrote:
The largest possible cube is enclosed in a cylinder and has volume 64. What is the volume of the cylinder if its height is 12?

A. 384π
B. 192π
C. 144π
D. 96π
E. 48π

Volume of Cube=64

a^3=64 ==> a=4

volume of the cylinder = πr^2(h)

Volume = π*8*12 = 96π

Hence D
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Re: The largest possible cube is enclosed in a cylinder and has volume 64.  [#permalink]

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17 Sep 2018, 23:08
Ok . Here is my take. We know the volume of cube is 64 . So each side of cube will be 4 .

If we place the largest possible cube in a cylinder then the condition would be only this, The edge of all sides of cube will touch the cylinder circular wall. Hence a circle with a centre can be drawn where the radius will be the diagonal of square formed by cube.
So we have a square of 4* 4 which is circumscribed by a circle. hence the diagonal of square will be diameter of cylindrical circular part.
I am attaching the screenshot for reference .
Attachments

File comment: Solution and diagram

WhatsApp Image 2018-09-18 at 11.30.57 AM.jpeg [ 125.62 KiB | Viewed 395 times ]

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Re: The largest possible cube is enclosed in a cylinder and has volume 64.   [#permalink] 17 Sep 2018, 23:08
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