To determine how much space the truck service needs to transport the 75 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 given by:
\[ V = s^3 \]
where \( s \) is the side length of the cube.
Given that the side length \( s \) 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:
- \( 18 \times 18 = 324 \)
- \( 324 \times 18 = 5,832 \)
Thus, the volume of one box is \( 5,832 , \text{in}^3 \).
Now, to find the total volume for 75 boxes, we multiply the volume of one box by the number of boxes:
\[ \text{Total Volume} = 75 \times 5,832 \]
Calculating this:
- \( 75 \times 5,832 = 437,400 , \text{in}^3 \)
Thus, the total space needed to transport the 75 boxes is \( 437,400 , \text{in}^3 \).
The correct response is:
437,400 in. cubed.