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14 Jul 2006, 15:09
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A large cube 10 cm on a side is composed of cubes 1 cm on a side. The outside of the large cube is painted red and then all of the individual 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
again... fastest way to solve this
:
A) 1:6
B) 1:5
C) 1:4
D) 1:3
E) 1:2
again... fastest way to solve this
:
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14 Jul 2006, 17:23
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Don’t know if it's the fastest way but it work for me.
Total 1cm cubes = 10x10x10=1000
Total 1cm cubes with only one face painted red=8x10x6=480
Total 1cm cubes that are painted on three sides to be consider=4+4=8
Probability = 488/1000 is close to 1/2 -E-
Total 1cm cubes = 10x10x10=1000
Total 1cm cubes with only one face painted red=8x10x6=480
Total 1cm cubes that are painted on three sides to be consider=4+4=8
Probability = 488/1000 is close to 1/2 -E-
14 Jul 2006, 17:35
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Maybe it is a faster way to consider the interior of the large cube.
We know that we have 10*10*10=1000 small cubes.
(10-2)*(10-2)*(10-2)=8*8*8=512 of the small cubes are in the interior of the large cube.
(1000-512)/1000=488/1000 is approximately equal to 1/2.
Hence (E).
We know that we have 10*10*10=1000 small cubes.
(10-2)*(10-2)*(10-2)=8*8*8=512 of the small cubes are in the interior of the large cube.
(1000-512)/1000=488/1000 is approximately equal to 1/2.
Hence (E).
