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

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Math Expert
Joined: 02 Sep 2009
Posts: 56226
What is the maximum number of spheres of radius 2 can fit into a cube  [#permalink]

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11 Sep 2018, 02:06
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Difficulty:

35% (medium)

Question Stats:

71% (01:47) correct 29% (01:54) wrong based on 35 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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Math Expert
Joined: 02 Aug 2009
Posts: 7764
Re: What is the maximum number of spheres of radius 2 can fit into a cube  [#permalink]

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11 Sep 2018, 02:35
1
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, 06:55
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, 09:01
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  [#permalink]

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20 May 2019, 11:33
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

Why my approach of dividing the given volume of cube (512 units) by volume of a sphere is not correct ?
Math Expert
Joined: 02 Sep 2009
Posts: 56226
Re: What is the maximum number of spheres of radius 2 can fit into a cube  [#permalink]

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21 May 2019, 00:16
pandajee wrote:
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

Why my approach of dividing the given volume of cube (512 units) by volume of a sphere is not correct ?

When you place spheres into a cube, you get an empty spaces in the cube which are not occupied with the spheres (you cannot squeeze spheres to make them cubes). Your method does not take these empty spaces into the account.
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Re: What is the maximum number of spheres of radius 2 can fit into a cube   [#permalink] 21 May 2019, 00:16
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