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17 Sep 2018, 21:59
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D
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Difficulty:
55%
(hard)
Question Stats:
56% (01:42) correct
44%
(01:35)
wrong
based on 55
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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 .
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File comment: Solution and diagram
WhatsApp Image 2018-09-18 at 11.30.57 AM.jpeg [ 125.62 KiB | Viewed 2050 times ]
