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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: 58443
What is the maximum number of spheres of radius 2 can fit into a cube  [#permalink]

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07 Sep 2018, 01:39
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Difficulty:

55% (hard)

Question Stats:

54% (01:43) correct 46% (01:37) wrong based on 51 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. 0
B. 1
C. 3
D. 4
E. 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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07 Sep 2018, 02:52
Bunuel wrote:
What is the maximum number of spheres of radius 2 can fit into a cube of volume 512 units?

A. 0
B. 1
C. 3
D. 4
E. 8

Volume of cube = $$a^3 = 512$$

i.e. $$a = 8$$

every dimension of 8 unit can accomodate 8/4 spheres where 4 is the diameter of the sphere

i.e. total such spheres = (8/4)*(8/4)*(8/4) = 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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18 Sep 2018, 21:15
Bunuel Can you please provide the solution for this? Thanks in advance.

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

A. 0
B. 1
C. 3
D. 4
E. 8
Re: What is the maximum number of spheres of radius 2 can fit into a cube   [#permalink] 18 Sep 2018, 21:15
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