SOLUTION: A large cube is dipped into red paint and divided into 216 smaller congruent cubes. one of the smaller cube is then randomly selected. What is the probability that the cube selecte

Question 370267: A large cube is dipped into red paint and divided into 216 smaller congruent cubes. one of the smaller cube is then randomly selected. What is the probability that the cube selected will have at least 25% of its surface area painted red?
express answers as a common fraction
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
The surface are of a cube with sides of 3 = 6*3^2 = 54, so after the division, 54 of the cubes will have some paint on them.
The center cube of each face will have only one of its faces painted, 6 of those, so 48 cubes will have 2 or 3 faces painted, giving them more than 25% coverage.
48/216 = 2/9
RELATED QUESTIONS
A cube measuring 6cm a side is painted red, and then cut up into 216 smaller cubes each... (answered by ikleyn)

A cube measuring 6cm a side is painted red, and then cut up into 216 smaller cubes each... (answered by ikleyn)

Please help me to get how to solve this problem. Thank you! Here it is... There are... (answered by scott8148)

A large cube is painted red and then cut into 1000 congruent small cubes. How many of... (answered by macston)

A cube is painted red and then cut into 1000 identical smaller cubes. How many of these... (answered by Edwin McCravy)

A 12 centimeter cube (i.e. 12x12x12) was painted red on the outside. The cube was then... (answered by rcmcc)

Twenty seven white unit cubes are stacked into one large cube. The surface of the large... (answered by Jk22)

A cube has an angle length of 4 inches. The cube is painted red all over and then cut... (answered by Alan3354)

A cube has an edge length of 4 inches. The cube is painted red all over and then cut... (answered by ikleyn)