A large cube is built from centimeters cubes. The faces of the large cube are painted .Of the centimeter cubes, 1000 are unpainted
see the other post.
To determine the length of the side of the large cube, we need to find the number of cubes on each face. Since there are 6 faces on a cube, we can assume that each face has the same number of cubes.
Let's call the length of the side of the large cube "x". The number of cubes on each face can be represented as x², because there are x cubes on each side, and there are x sides.
Given that 1000 cubes are unpainted, and all the other cubes are painted, we can set up the following equation:
x³ - 1000 = total number of painted cubes
Since we know that there are x² cubes on each face, and there are 6 faces, the total number of painted cubes would be 6 * x².
Now we can rewrite the equation as:
x³ - 1000 = 6 * x²
To solve this equation, we can rearrange it to:
x³ - 6 * x² - 1000 = 0
Once we have this equation, we can solve it using various methods like factoring, graphing, or using numerical methods like Newton's method.
After finding the value of x, we can conclude that the length of the side of the large cube is x centimeters.