How do you calculate the surface area of a cube?

The surface area of a cube is calculated using the formula SA = 6s², where s is the length of one side. This accounts for all six faces of the cube.

If a die has 6 faces numbered from 1 to 6, what is the probability of rolling a number greater than 4?

There are 2 favorable outcomes (5 and 6) out of 6 possible outcomes. Therefore, the probability is P = 2/6 = 1/3.

How many total outcomes are there when rolling two six-sided dice?

When rolling two six-sided dice, each die has 6 faces, resulting in a total of 6 * 6 = 36 possible outcomes.

What is the opposite face of a die showing 3?

The opposite face of a die showing 3 is 4, as the sum of opposite faces equals 7.

In a 5x5x5 cube, how many smaller cubes have exactly 2 painted faces?

The number of smaller cubes with exactly 2 painted faces is given by the formula 12(n - 2), resulting in 12(5 - 2) = 36.

If a cube is painted on all faces and then cut into 1x1x1 cubes, how many cubes have no painted faces?

The number of 1x1x1 cubes with no painted faces is (n - 2)³, where n is the side length of the original cube.

When rolling three six-sided dice, what is the probability of rolling at least one 6?

Probability of at least one 6 is 91/216.

• Rolling three dice is common.

• Complementary probability simplifies calculations.

• Understanding probabilities aids in decision-making.

What is the total number of edges in a cube?

A cube has a total of 12 edges.

If a die is rolled twice, what is the probability of rolling the same number both times?

The probability of rolling the same number on two rolls is P = 6/36 = 1/6, since there are 6 favorable outcomes.

If two dice are rolled, what is the probability of rolling a sum of 2?

The only combination for a sum of 2 is (1,1), giving a probability of P = 1/36.

How many corner cubes are there in a 3x3x3 cube?

8 corner cubes.