A carton can hold 1,000 unit cubes that measure 1 inch by 1 inch. Describe the dimensions of the carton using unit cubes?
10 * 10 * 10 = 1,000
The dimension of the cartoon are 10 inches to 10 inches
The dimensions are 10x10x10
To determine the dimensions of the carton using unit cubes, we need to find the length, width, and height of the carton in terms of the number of unit cubes it can hold.
Given that a carton can hold 1,000 unit cubes, let's first find the length. Each cube measures 1 inch by 1 inch, so if we stack the cubes in a straight line, the length of the carton would be equal to the number of cubes it can hold, which is 1,000 cubes.
Next, let's determine the width. Assuming we stack the cubes in layers, the width of the carton would represent the number of cubes in each layer. Since the length is 1,000 cubes, it would be more convenient to express this value as a product of two numbers. To determine the width, we can try dividing 1,000 by different numbers until we find a factor that gives us a whole number.
Dividing 1,000 by 2 gives us 500, which is a whole number. Thus, the width of the carton is 500 cubes.
Finally, to find the height, we can divide the total number of cubes, 1,000, by the length and width.
Dividing 1,000 by 1,000 (length) and 500 (width) gives us 1, which is a whole number. Therefore, the height of the carton is 1 cube.
In summary, the carton's dimensions, using unit cubes, are:
- Length: 1,000 cubes
- Width: 500 cubes
- Height: 1 cube