A large cube 10cm on a side is composed of smaller cubes 1 : DS Archive
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# A large cube 10cm on a side is composed of smaller cubes 1

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VP
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A large cube 10cm on a side is composed of smaller cubes 1 [#permalink]

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18 Nov 2006, 18:11
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A large cube 10cm on a side is composed of smaller cubes 1 cm on a side. The large cube is
printed red on its outside surfaces and then all the cubes are mixed in a drum.
If one cube is selected randomly, which of the following is the approximate probability
that the cube will have at least one red face?

A) 1:6
B) 1:5
C) 1:4
D) 1:3
E) 1:2
Senior Manager
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18 Nov 2006, 19:00
Is it 1 : 2

Explanation
Total smaller cubes = 10^3
Number of inner cubes, which are not painted = (10 â€“ 2)^3
So probability 10^3 â€“ 8^3 : 10^3 => 488 : 1000 = 1 : 2 (approx)
VP
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18 Nov 2006, 23:16
agree with E.

the painted are 488 out of total 1000.
Manager
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18 Nov 2006, 23:56
Quick question
Here you said

Quote:
Total smaller cubes = 10^3

I don't think there are a 1000 cubes inside of this cube?
Or are you talking about total area?
The above equation is for volume which is not relevant, we are looking for surface area right?
VP
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19 Nov 2006, 02:26
It is not surface area, nor is it volume.

you need to count the no of small cubes.
VP
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19 Nov 2006, 20:01
anindyat wrote:
Is it 1 : 2

Explanation
Total smaller cubes = 10^3
Number of inner cubes, which are not painted = (10 â€“ 2)^3
So probability 10^3 â€“ 8^3 : 10^3 => 488 : 1000 = 1 : 2 (approx)

Can you please tell me how you arrived at that? Totally lost
VP
Joined: 21 Mar 2006
Posts: 1134
Location: Bangalore
Followers: 3

Kudos [?]: 40 [0], given: 0

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19 Nov 2006, 20:04
anindyat wrote:
Is it 1 : 2

Explanation
Total smaller cubes = 10^3
Number of inner cubes, which are not painted = (10 â€“ 2)^3
So probability 10^3 â€“ 8^3 : 10^3 => 488 : 1000 = 1 : 2 (approx)

Can you please tell me how you arrived at that? Totally lost
Director
Joined: 18 Jul 2006
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19 Nov 2006, 23:24
kripalkavi wrote:
anindyat wrote:
Is it 1 : 2

Explanation
Total smaller cubes = 10^3
Number of inner cubes, which are not painted = (10 â€“ 2)^3
So probability 10^3 â€“ 8^3 : 10^3 => 488 : 1000 = 1 : 2 (approx)

Can you please tell me how you arrived at that? Totally lost

In simple terms, there is 8x8x8 cube inside 10x10x10 which remains unpainted (as top and bottom i.e. 1st and 10th cubes are painted)
VP
Joined: 21 Mar 2006
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20 Nov 2006, 00:16
Juaz wrote:
kripalkavi wrote:
anindyat wrote:
Is it 1 : 2

Explanation
Total smaller cubes = 10^3
Number of inner cubes, which are not painted = (10 â€“ 2)^3
So probability 10^3 â€“ 8^3 : 10^3 => 488 : 1000 = 1 : 2 (approx)

Can you please tell me how you arrived at that? Totally lost

In simple terms, there is 8x8x8 cube inside 10x10x10 which remains unpainted (as top and bottom i.e. 1st and 10th cubes are painted)

Thanks! As youy might have guessed, OA is E
20 Nov 2006, 00:16
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