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655-705 (Hard)|   Geometry|      
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Bunuel
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The largest possible cube is enclosed in a cylinder and has volume 64. 17 Sep 2018, 21:59
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55% (hard)

Question Stats:

56% (01:40) correct 44% (01:33) wrong based on 57 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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D
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The largest possible cube is enclosed in a cylinder and has volume 64. 17 Sep 2018, 22:07
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Bunuel
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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Volume of Cube=64

a^3=64 ==> a=4

Radius =2\sqrt{2}

volume of the cylinder = πr^2(h)

Volume = π*8*12 = 96π

Hence D
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The largest possible cube is enclosed in a cylinder and has volume 64. 17 Sep 2018, 23:08
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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 .
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File comment: Solution and diagram
WhatsApp Image 2018-09-18 at 11.30.57 AM.jpeg
WhatsApp Image 2018-09-18 at 11.30.57 AM.jpeg [ 125.62 KiB | Viewed 2124 times ]

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The largest possible cube is enclosed in a cylinder and has volume 64. 19 Sep 2018, 01:16
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Bunuel
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
Show more

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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The largest possible cube is enclosed in a cylinder and has volume 64. 07 Jun 2023, 00:03
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