A large cube is made up of 27 small cubes. Each of the six faces of the large cube has 9 small squares. Each small square has an area of 144 square millimeters.
What is the length of each side of the large cube?
small squares are 12x12
cube faces are 3x3 of 12x12 = 36x36
To find the length of each side of the large cube, we need to determine the length of each side of the small cubes that make up the large cube.
Since each small square has an area of 144 square millimeters, the length of one side of a small square can be found by taking the square root of 144:
√144 = 12 millimeters
Since there are 27 small cubes in the large cube and each small cube has 6 faces, the large cube is made up of 6 x 27 = 162 small squares.
Let's suppose the length of each side of the large cube is 'x'. Then, the total area of all the small squares in the large cube can be calculated as:
162 * (x^2) = 6 * (x^2) * 27
Simplifying further:
162x^2 = 162x^2
We can see that the equation is true for any value of 'x'. It means the equation is satisfied for all values of 'x'. Therefore, the length of each side of the large cube can be any value.
To find the length of each side of the large cube, we can start by determining the side length of one of the small cubes.
Since each small square has an area of 144 square millimeters, the side length of a small square can be found by taking the square root of the area.
√144 = 12 millimeters
Therefore, each side of a small square is 12 millimeters long.
Since there are 27 small cubes in the large cube, we can arrange them in a 3x3x3 structure, with 3 cubes on each side.
To find the length of the large cube, we can multiply the side length of a small cube by the number of cubes on one side.
12 millimeters x 3 = 36 millimeters
Hence, the length of each side of the large cube is 36 millimeters.