+1245
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?
+9479 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
+9479 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
