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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?

Mar 19, 2018

#1
+7543
+2

Let each small cube be  1 cubic unit.

volume of big cube  =  125 cubic units

side length of big cube  =  125^(1/3) units  =  5  units

surface area of big cube  =  total painted area  =  6 * 5^2  =  150  sq units

surface area of one small cube  =  6  sq units

combined surface area of small cubes  =  125 * 6  sq units  =  750 sq units

Each face of small cube is 1 sq unit.

There are a total of 150 sq units that are painted, so there are a total of 150 faces with paint on them.

There are a total of 750 sq units, so there are a total of 750 faces.

The probability that a randomly selected face is one with paint on it  =  150/750  =  1/5

Mar 19, 2018

#1
+7543
+2

Let each small cube be  1 cubic unit.

volume of big cube  =  125 cubic units

side length of big cube  =  125^(1/3) units  =  5  units

surface area of big cube  =  total painted area  =  6 * 5^2  =  150  sq units

surface area of one small cube  =  6  sq units

combined surface area of small cubes  =  125 * 6  sq units  =  750 sq units

Each face of small cube is 1 sq unit.

There are a total of 150 sq units that are painted, so there are a total of 150 faces with paint on them.

There are a total of 750 sq units, so there are a total of 750 faces.

The probability that a randomly selected face is one with paint on it  =  150/750  =  1/5

hectictar Mar 19, 2018