Final answer:
The stack of 1 cm³ cubes needed to fill a 1m x 2m x 5m box would be 100 kilometers high, considering there are 10,000,000 cm³ in the box that would each be replaced by a 1 cm³ cube.
Step-by-step explanation:
To calculate the height of the stack of 1 cm³ cubes needed to fill a 1m x 2m x 5m box, first determine the volume of the box in cubic centimeters. The box's volume is 1m x 2m x 5m = 10m³. Since there are 1,000,000 cm³ in 1m³, the box's volume in cubic centimeters is 10m³ x 1,000,000 cm³/m³ = 10,000,000 cm³.
Each small cube has a volume of 1 cm³, so the number of small cubes needed to fill the box is equal to the volume of the box. Therefore, 10,000,000 small cubes are needed. To find out how high the stack would be in kilometers, we convert the total number of cubes into meters and then into kilometers. Since there are 100 cm in a meter, the height of the stack in meters would be 10,000,000 cm / 100 cm/m = 100,000 m. To convert meters into kilometers, we use the conversion factor of 1 km = 1000 m. Therefore, the stack would be 100,000 m / 1000 m/km = 100 km high.