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

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A large cube 10cm on a side is composed of smaller cubes 1 [#permalink] New post 15 May 2004, 16:41
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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
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Re: PS-37 [#permalink] New post 15 May 2004, 17:13
hallelujah1234 wrote:
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


# of small cubes painted on one side=surface area of large cube/are of one side of small cube=6*10*10=600/1=600
total small cubes=10*10*10=1000
P(cube will have at least one red face)=600/1000=3/5 :shock:
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Re: PS-37 [#permalink] New post 17 May 2004, 11:33
Answer = (10^3-8^3)/10^3 = (5^3-4^3)/5^3 = (125-64)/125 ~ 1/2
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 [#permalink] New post 17 May 2004, 13:50
well, there are 10^3 cubes. How many of them are visible? In order to count the latter, it is better count the #unvisible ones.

#unvisibles = (10-2)(10-2)(10-2) = 8^3
#visible ones(or red painted) = 10^3 - 8^3
  [#permalink] 17 May 2004, 13:50
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