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?

Lightning
Mar 19, 2018

#1**+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

#1**+2 **

Best Answer

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