Math question. PLeaz help and explain well?

Question

A 3 cm cube is first painted red and then cut into 27, 1 cm cubes.

All 27, 1 cm cubes are places in a bag and 1 is drawn out at random

What is the probability that the cube has paint on:

0 sides?

1 side?

2 sides?

3 sides?

4 sides?

Answer 1

3 Sides

Answer 2

Just suppose we give number to all the cubes like this:

first row:

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| 1 | 2 | 3|

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| 4 | 5 | 6|

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| 7 | 8 | 9|

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second row:

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|10|11|12|

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|13|14|15|

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|16|17|18|

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third row:

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|19|20|21|

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|22|23|24|

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|25|26|27|

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We know that the cubes that are painted is the one whose surface is visible form outside, that is all of them except cube no. 14. So the probability we get the one whit 0 sides painted is 1/27

1 side painted can be got from no 11 , 13,15,17 so it has 4/27 probability

2 sides painted can be got from no 2, 4,6,8 ,10,12,16,18,20,22,24,26. So it has 12/27 probability.

3 sides painted can be got from no 1,3,7,9,19,22,25,27, so there is 6/27 probability. But there won't be a cube with 4 painted sides. So it has 0 probability

Answer 3

well you have to place the cube together after it has been cut in your mind (if that makes sense)

i would draw a cube, and then divide it into 27 parts if i were you.

then you can see it better.

for me to explain it to you, number the cubes 1 - 9, like on a phone, on the side facing you. something like this, but with horizantal lines as well:

            _____________

            |.\ .................. \

            |...---------------------

            |...|.1...|...2...|...3.|

            |...|.4...|...5...|...6.|

            \...|.7...|...8...|...9.|

------------------------

there is only one with 0 sides painted, the one in the very middle of the big cube. the one right behind block number 5. so 1 out of 27 cubes have one side painted.

the only one with one side painted is number 5, and there are six of those, so six out of 27 will have one side painted.

numbers 2, 4, 6, and 8 have two sides painted. and there are 12 of those (i believe) so 12 out of 27 have two sides painted.

the ones in the very corner, numbers 1, 3, 7, and 9, have 3 sides painted, (or open to the outside). there are eight corners on a cube, so 8 out of 27 have 3 sides painted.

I'm pretty sure there can't be any with four sides painted, so 0 out of 27.

Just to double check, add all the numbers and you get 27 out of 27...

hope this helped.

jeez you have no idea how long it took me to make that cube and then figure out how many 2 sided ones there are... *phew*

bye!

hope this helped!

Answer 4

0 sides- 1 cube (the center one)

1 side- 6 cubes (the center of each face)

2 sides- 12 cubes (the middle cube of each edge)

3 sides- 8 cubes (every corner cube)

4 sides- none

Now, the probability part. It's the number of cubes with that possibility/the total number of cubes, so it would be something over 27 for all of them. I'm sure you can work that part out by yourself.

Answer 5

0 sides - only the cube at the very center is not painted = 1/27

1 side - only the center cube of each of the 6 sides of the 3cm cube = 6/27

2 sides - only the cubes at the edge of the 3cm cube = 12/27

3 sides - only the cubes at the corner of the 3cm cube = 8/27

4 sides - not possible = 0

1+6+12+8=27 <= that covers all the possibilities