Final answer:
The box of cubes, when stacked, would reach a height of 5000 kilometers. This is calculated by finding the number of 1mm³ cubes that can fit into a box measuring 1m x 5m and multiplying that number by the height of each cube.
Step-by-step explanation:
To determine how high a stack of cubes would reach, we first need to calculate the total volume of a box with dimensions of 1m by 5m. Assuming the student meant the height of the box is also 1m (as it wasn't stated), the volume would be 1m x 1m x 5m = 5m³. If each small cube has a volume of 1mm³, which is equivalent to 1 x 10⁻9 m³ (since there are 1,000mm in a meter), then we can calculate the number of small cubes that would fit into the box: dividing the volume of the large box by the volume of a single cube gives us 5m³ / 1 x 10⁻9 m³ per cube = 5 x 10⁹ cubes in total.
Now, if these cubes were stacked on top of each other to form a tower, the height would be the number of cubes times the height of each cube. Since each cube is 1mm tall, or 1 x 10⁻3 meters, the total height of the stacked cubes would be 5 x 10⁹ cubes x 1 x 10⁻3 meters/cube = 5 x 10⁶ meters in height. To convert meters to kilometers, we divide by 1,000, resulting in a height of 5 x 10 kilometers or 5000 kilometers.