To determine the space needed to transport the 75 boxes, we first need to calculate the volume of a single box. The formula for the volume of a cube is:
\[ V = s^3 \]
where \( s \) is the side length of the cube.
Given that the side length \( s \) of the boxes is 18 inches, we can calculate the volume of one box:
\[ V = 18^3 \]
Calculating \( 18^3 \):
\[ 18 \times 18 = 324 \] \[ 324 \times 18 = 5,832 , \text{in}^3 \]
So, the volume of one box is 5,832 cubic inches.
Now, to find the total volume for 75 boxes, we multiply the volume of one box by 75:
\[ \text{Total Volume} = 75 \times 5,832 \]
Calculating that:
\[ 75 \times 5,832 = 437,400 , \text{in}^3 \]
Therefore, the total space needed to transport the 75 boxes is 437,400 in.³.