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A cube is painted red on all six sides, then cut into 125 smaller congruent cubes.

A small cube is selected at random and rolled. What is the probability that it has a red side facing up?

Jeff123  Sep 13, 2017

Best Answer 

 #2
avatar+90212 
+2

Thanks, Chozerr,

It is really good that you had a go AND that you stated your lack of confidence.

It is not a really easy question... I'll give it a go

 

 

First, like you said, the big cube is cut into 5*5*5

Starting with the top row and working down, I am going to count how many red sides each little cube has.

 

Top and bottom rows

3*4+2*12+9 = 12+108+9 = 129 red sides on top row and 129 on the bottom one too

3 2 2 2 3
2 1 1 1 2
2 1 1 1 2
2 1 1 1 2
3 2 2 2 3

 

3 rows in the middle

3*(2*4+1*12) = 60 other red sides

2 1 1 1 2
1 0 0 0 1
1 0 0 0 1
1 0 0 0 1
2 1 1 1 2

 

Total number of red sides = 129+129+60 = 318 red sides altogether

There are 125 little cubes so these have a total of 125*6 = 750 sides

 

So if you choose a little cube at random and roll it I think the probability of rolling a red is  318/750 = 53/125

 

I think this is correct but there might have been an easier way to do it. I am really not sure.  :)

Melody  Sep 13, 2017
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2+0 Answers

 #1
avatar+56 
+2

I'll start by saying that I am unsure whether my answer is correct.

 

You have a cube which is separated into 125 smaller cubes. This must mean that your cube is 5 smaller cubes long on each side. 

This means that the amount of colored small cube sides is 150 (calculated by doing 5*5*6) 

A number of sides in total is 750 (125*6) 

This would mean that the percentage of colored sides is 20%

So the probability is 1:5 or 20%.

 

Feel free to correct me if I'm wrong. :)

ChoZerr  Sep 13, 2017
 #2
avatar+90212 
+2
Best Answer

Thanks, Chozerr,

It is really good that you had a go AND that you stated your lack of confidence.

It is not a really easy question... I'll give it a go

 

 

First, like you said, the big cube is cut into 5*5*5

Starting with the top row and working down, I am going to count how many red sides each little cube has.

 

Top and bottom rows

3*4+2*12+9 = 12+108+9 = 129 red sides on top row and 129 on the bottom one too

3 2 2 2 3
2 1 1 1 2
2 1 1 1 2
2 1 1 1 2
3 2 2 2 3

 

3 rows in the middle

3*(2*4+1*12) = 60 other red sides

2 1 1 1 2
1 0 0 0 1
1 0 0 0 1
1 0 0 0 1
2 1 1 1 2

 

Total number of red sides = 129+129+60 = 318 red sides altogether

There are 125 little cubes so these have a total of 125*6 = 750 sides

 

So if you choose a little cube at random and roll it I think the probability of rolling a red is  318/750 = 53/125

 

I think this is correct but there might have been an easier way to do it. I am really not sure.  :)

Melody  Sep 13, 2017

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