To find the space needed to transport 75 boxes, we first need to calculate the volume of one cube and then multiply it by the number of boxes.
The formula for the volume \( V \) of a cube is: \[ V = s^3 \] where \( s \) is the side length of the cube.
Given that the side length of each box is 18 inches, we can calculate the volume of one box: \[ V = 18^3 = 18 \times 18 \times 18 \]
Calculating this step by step: \[ 18 \times 18 = 324 \] Then, \[ 324 \times 18 = 5,832 \text{ cubic inches} \]
Now, to find the total volume for 75 boxes: \[ \text{Total Volume} = 75 \times 5,832 = 437,400 \text{ cubic inches} \]
Thus, the amount of space the service will need to transport the boxes is: 437,400 in. cubed.