To find the space needed to transport the boxes, we first need to calculate the volume of a single box and then multiply that 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 \( s \) is 18 inches, we calculate the volume of one box:
\[ V = 18^3 = 18 \times 18 \times 18 \]
Calculating this step-by-step:
- \( 18 \times 18 = 324 \)
- \( 324 \times 18 = 5,832 \) cubic inches
Now that we have the volume of one box, we need to calculate the total volume required for 75 boxes:
\[ \text{Total Volume} = 75 \times 5,832 \]
Calculating this:
\[ 75 \times 5,832 = 437,400 \text{ cubic inches} \]
So, the service will need a total space of 437,400 cubic inches to transport the boxes.
The correct response is:
437,400 in. cubed