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17 Sep 2018, 21:59
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
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
A. 384π
B. 192π
C. 144π
D. 96π
E. 48π
17 Sep 2018, 22:07
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Bunuel
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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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 .
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 2126 times ]
19 Sep 2018, 01:16
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Bunuel
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 = \(\pi*r^2 * h = \pi * (2\sqrt{2})^2 * 12 = 96\pi\)
