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

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VP
Joined: 21 Mar 2006
Posts: 1135
Location: Bangalore
Followers: 2

Kudos [?]: 28 [0], given: 0

A large cube 10cm on a side is composed of smaller cubes 1 [#permalink]  18 Nov 2006, 18:11
00:00

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(N/A)

Question Stats:

100% (02:05) correct 0% (00:00) wrong based on 1 sessions
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
Joined: 08 Jun 2006
Posts: 342
Location: Washington DC
Followers: 1

Kudos [?]: 23 [0], given: 0

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
Joined: 25 Jun 2006
Posts: 1175
Followers: 2

Kudos [?]: 72 [0], given: 0

agree with E.

the painted are 488 out of total 1000.
Manager
Joined: 08 May 2004
Posts: 158
Location: Pittsburgh
Followers: 1

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

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
Joined: 25 Jun 2006
Posts: 1175
Followers: 2

Kudos [?]: 72 [0], given: 0

It is not surface area, nor is it volume.

you need to count the no of small cubes.
VP
Joined: 21 Mar 2006
Posts: 1135
Location: Bangalore
Followers: 2

Kudos [?]: 28 [0], given: 0

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: 1135
Location: Bangalore
Followers: 2

Kudos [?]: 28 [0], given: 0

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
Posts: 531
Followers: 1

Kudos [?]: 30 [0], given: 0

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
Posts: 1135
Location: Bangalore
Followers: 2

Kudos [?]: 28 [0], given: 0

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
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