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What is the maximum number of spheres of radius 2 can fit into a cube

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What is the maximum number of spheres of radius 2 can fit into a cube  [#permalink]

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11 Sep 2018, 01:06
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Difficulty:

45% (medium)

Question Stats:

73% (01:15) correct 27% (01:00) wrong based on 15 sessions

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What is the maximum number of spheres of radius 2 can fit into a cube of volume 512 units?

A. 2
B. 3
C. 6
D. 8
E. 16

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Joined: 02 Aug 2009
Posts: 7028
Re: What is the maximum number of spheres of radius 2 can fit into a cube  [#permalink]

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11 Sep 2018, 01:35
Bunuel wrote:
What is the maximum number of spheres of radius 2 can fit into a cube of volume 512 units?

A. 2
B. 3
C. 6
D. 8
E. 16

Now the sphere will occupy the same space as a cube in which it exactly fits in and the dia of sphere and side of cube are same...

So each sphere of radius 2 or dia 4 will exactly fit into a cube of length 4..
Or the volume =4*4*4..

Total volume of bigger cube=512

So number of spheres that can fit in = 512/(4*4*4)=8

D
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Re: What is the maximum number of spheres of radius 2 can fit into a cube  [#permalink]

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11 Sep 2018, 05:55
Bunuel wrote:
What is the maximum number of spheres of radius 2 can fit into a cube of volume 512 units?

A. 2
B. 3
C. 6
D. 8
E. 16

Volume of cube = 512
therefore Side=8 units

Dia: 4
One sphere will take 4 units length breadth and height each.

Therefore, there will be $$\frac{8}{4} =2$$ along the length, breadth and height each.
therefore total no of spheres=$$2*2*2$$
=8

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Re: What is the maximum number of spheres of radius 2 can fit into a cube  [#permalink]

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11 Sep 2018, 08:01
volume of cube=512=8*8*8
side length of cube=8
sphere diameter=2*2=4
So along one side of cube, 2 spheres of radius 2 can fit. Similarly 2 spheres along the other side and 2 spheres along the third side of cube.
So total number of spheres in cube would be 2*2*2=8

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Re: What is the maximum number of spheres of radius 2 can fit into a cube &nbs [#permalink] 11 Sep 2018, 08:01
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